diff --git a/crates/swc/tests/fixture/issues-6xxx/6739/input/.swcrc b/crates/swc/tests/fixture/issues-6xxx/6739/input/.swcrc
new file mode 100644
index 000000000000..9381cfabfff4
--- /dev/null
+++ b/crates/swc/tests/fixture/issues-6xxx/6739/input/.swcrc
@@ -0,0 +1,8 @@
+{
+    "jsc": {
+        "parser": {
+            "syntax": "typescript",
+            "tsx": false
+        }
+    }
+}
\ No newline at end of file
diff --git a/crates/swc/tests/fixture/issues-6xxx/6739/input/index.ts b/crates/swc/tests/fixture/issues-6xxx/6739/input/index.ts
new file mode 100644
index 000000000000..d1e85649e624
--- /dev/null
+++ b/crates/swc/tests/fixture/issues-6xxx/6739/input/index.ts
@@ -0,0 +1 @@
+console.log(x < y >>> z);
diff --git a/crates/swc/tests/fixture/issues-6xxx/6739/output/index.js b/crates/swc/tests/fixture/issues-6xxx/6739/output/index.js
new file mode 100644
index 000000000000..d1e85649e624
--- /dev/null
+++ b/crates/swc/tests/fixture/issues-6xxx/6739/output/index.js
@@ -0,0 +1 @@
+console.log(x < y >>> z);
diff --git a/crates/swc/tests/fixture/issues-6xxx/6739/output/index.ts b/crates/swc/tests/fixture/issues-6xxx/6739/output/index.ts
new file mode 100644
index 000000000000..d1e85649e624
--- /dev/null
+++ b/crates/swc/tests/fixture/issues-6xxx/6739/output/index.ts
@@ -0,0 +1 @@
+console.log(x < y >>> z);
diff --git a/crates/swc_ecma_parser/src/lexer/state.rs b/crates/swc_ecma_parser/src/lexer/state.rs
index 3f588eda7686..4cf9fb7e523b 100644
--- a/crates/swc_ecma_parser/src/lexer/state.rs
+++ b/crates/swc_ecma_parser/src/lexer/state.rs
@@ -329,7 +329,7 @@ impl<'a, I: Input> Iterator for Lexer<'a, I> {
                 if c == '<' {
                     self.input.bump();
                     return Ok(Some(tok!('<')));
-                } else if c == '>' {
+                } else if c == '>' && !self.ctx.prefer_bin_op_over_type_arg_closing {
                     self.input.bump();
                     return Ok(Some(tok!('>')));
                 }
diff --git a/crates/swc_ecma_parser/src/lib.rs b/crates/swc_ecma_parser/src/lib.rs
index 03ec34504ff9..b523edfabb70 100644
--- a/crates/swc_ecma_parser/src/lib.rs
+++ b/crates/swc_ecma_parser/src/lib.rs
@@ -375,6 +375,10 @@ pub struct Context {
     ignore_else_clause: bool,
 
     disallow_conditional_types: bool,
+
+    /// Used for parsing `>`. If true, `>>` and `>>>` are parsed as binary
+    /// operators.
+    prefer_bin_op_over_type_arg_closing: bool,
 }
 
 #[derive(Debug, Clone, Copy, Default)]
diff --git a/crates/swc_ecma_parser/src/parser/expr.rs b/crates/swc_ecma_parser/src/parser/expr.rs
index c528113cbc24..3ad445d9c87a 100644
--- a/crates/swc_ecma_parser/src/parser/expr.rs
+++ b/crates/swc_ecma_parser/src/parser/expr.rs
@@ -671,7 +671,11 @@ impl<I: Tokens> Parser<I> {
         return_if_arrow!(self, obj);
 
         let type_args = if self.syntax().typescript() && is!(self, '<') {
-            self.try_parse_ts_type_args()
+            self.with_ctx(Context {
+                prefer_bin_op_over_type_arg_closing: true,
+                ..self.ctx()
+            })
+            .try_parse_ts_type_args()
         } else {
             None
         };
diff --git a/crates/swc_ecma_parser/src/parser/typescript.rs b/crates/swc_ecma_parser/src/parser/typescript.rs
index 4a4c990120b1..70965116ff86 100644
--- a/crates/swc_ecma_parser/src/parser/typescript.rs
+++ b/crates/swc_ecma_parser/src/parser/typescript.rs
@@ -557,7 +557,11 @@ impl<I: Tokens> Parser<I> {
     pub(super) fn try_parse_ts_type_args(&mut self) -> Option<Box<TsTypeParamInstantiation>> {
         debug_assert!(self.input.syntax().typescript());
 
-        self.try_parse_ts(|p| {
+        self.with_ctx(Context {
+            prefer_bin_op_over_type_arg_closing: true,
+            ..self.ctx()
+        })
+        .try_parse_ts(|p| {
             let type_args = p.parse_ts_type_args()?;
             if is_one_of!(
                 p, '<', // invalid syntax
diff --git a/crates/swc_ecma_parser/tests/typescript/issue-6739/1.ts b/crates/swc_ecma_parser/tests/typescript/issue-6739/1.ts
new file mode 100644
index 000000000000..d1e85649e624
--- /dev/null
+++ b/crates/swc_ecma_parser/tests/typescript/issue-6739/1.ts
@@ -0,0 +1 @@
+console.log(x < y >>> z);
diff --git a/crates/swc_ecma_parser/tests/typescript/issue-6739/1.ts.json b/crates/swc_ecma_parser/tests/typescript/issue-6739/1.ts.json
new file mode 100644
index 000000000000..07cf524f3a85
--- /dev/null
+++ b/crates/swc_ecma_parser/tests/typescript/issue-6739/1.ts.json
@@ -0,0 +1,109 @@
+{
+  "type": "Script",
+  "span": {
+    "start": 1,
+    "end": 26,
+    "ctxt": 0
+  },
+  "body": [
+    {
+      "type": "ExpressionStatement",
+      "span": {
+        "start": 1,
+        "end": 26,
+        "ctxt": 0
+      },
+      "expression": {
+        "type": "CallExpression",
+        "span": {
+          "start": 1,
+          "end": 25,
+          "ctxt": 0
+        },
+        "callee": {
+          "type": "MemberExpression",
+          "span": {
+            "start": 1,
+            "end": 12,
+            "ctxt": 0
+          },
+          "object": {
+            "type": "Identifier",
+            "span": {
+              "start": 1,
+              "end": 8,
+              "ctxt": 0
+            },
+            "value": "console",
+            "optional": false
+          },
+          "property": {
+            "type": "Identifier",
+            "span": {
+              "start": 9,
+              "end": 12,
+              "ctxt": 0
+            },
+            "value": "log",
+            "optional": false
+          }
+        },
+        "arguments": [
+          {
+            "spread": null,
+            "expression": {
+              "type": "BinaryExpression",
+              "span": {
+                "start": 13,
+                "end": 24,
+                "ctxt": 0
+              },
+              "operator": "<",
+              "left": {
+                "type": "Identifier",
+                "span": {
+                  "start": 13,
+                  "end": 14,
+                  "ctxt": 0
+                },
+                "value": "x",
+                "optional": false
+              },
+              "right": {
+                "type": "BinaryExpression",
+                "span": {
+                  "start": 17,
+                  "end": 24,
+                  "ctxt": 0
+                },
+                "operator": ">>>",
+                "left": {
+                  "type": "Identifier",
+                  "span": {
+                    "start": 17,
+                    "end": 18,
+                    "ctxt": 0
+                  },
+                  "value": "y",
+                  "optional": false
+                },
+                "right": {
+                  "type": "Identifier",
+                  "span": {
+                    "start": 23,
+                    "end": 24,
+                    "ctxt": 0
+                  },
+                  "value": "z",
+                  "optional": false
+                }
+              }
+            }
+          }
+        ],
+        "typeArguments": null
+      }
+    }
+  ],
+  "interpreter": null
+}
diff --git a/crates/swc_ecma_parser/tests/typescript/issue-6739/2.tsx b/crates/swc_ecma_parser/tests/typescript/issue-6739/2.tsx
new file mode 100644
index 000000000000..d1e85649e624
--- /dev/null
+++ b/crates/swc_ecma_parser/tests/typescript/issue-6739/2.tsx
@@ -0,0 +1 @@
+console.log(x < y >>> z);
diff --git a/crates/swc_ecma_parser/tests/typescript/issue-6739/2.tsx.json b/crates/swc_ecma_parser/tests/typescript/issue-6739/2.tsx.json
new file mode 100644
index 000000000000..07cf524f3a85
--- /dev/null
+++ b/crates/swc_ecma_parser/tests/typescript/issue-6739/2.tsx.json
@@ -0,0 +1,109 @@
+{
+  "type": "Script",
+  "span": {
+    "start": 1,
+    "end": 26,
+    "ctxt": 0
+  },
+  "body": [
+    {
+      "type": "ExpressionStatement",
+      "span": {
+        "start": 1,
+        "end": 26,
+        "ctxt": 0
+      },
+      "expression": {
+        "type": "CallExpression",
+        "span": {
+          "start": 1,
+          "end": 25,
+          "ctxt": 0
+        },
+        "callee": {
+          "type": "MemberExpression",
+          "span": {
+            "start": 1,
+            "end": 12,
+            "ctxt": 0
+          },
+          "object": {
+            "type": "Identifier",
+            "span": {
+              "start": 1,
+              "end": 8,
+              "ctxt": 0
+            },
+            "value": "console",
+            "optional": false
+          },
+          "property": {
+            "type": "Identifier",
+            "span": {
+              "start": 9,
+              "end": 12,
+              "ctxt": 0
+            },
+            "value": "log",
+            "optional": false
+          }
+        },
+        "arguments": [
+          {
+            "spread": null,
+            "expression": {
+              "type": "BinaryExpression",
+              "span": {
+                "start": 13,
+                "end": 24,
+                "ctxt": 0
+              },
+              "operator": "<",
+              "left": {
+                "type": "Identifier",
+                "span": {
+                  "start": 13,
+                  "end": 14,
+                  "ctxt": 0
+                },
+                "value": "x",
+                "optional": false
+              },
+              "right": {
+                "type": "BinaryExpression",
+                "span": {
+                  "start": 17,
+                  "end": 24,
+                  "ctxt": 0
+                },
+                "operator": ">>>",
+                "left": {
+                  "type": "Identifier",
+                  "span": {
+                    "start": 17,
+                    "end": 18,
+                    "ctxt": 0
+                  },
+                  "value": "y",
+                  "optional": false
+                },
+                "right": {
+                  "type": "Identifier",
+                  "span": {
+                    "start": 23,
+                    "end": 24,
+                    "ctxt": 0
+                  },
+                  "value": "z",
+                  "optional": false
+                }
+              }
+            }
+          }
+        ],
+        "typeArguments": null
+      }
+    }
+  ],
+  "interpreter": null
+}