diff --git a/eslint/babel-eslint-parser/package.json b/eslint/babel-eslint-parser/package.json
index 0205facb646d..b64d7a051af3 100644
--- a/eslint/babel-eslint-parser/package.json
+++ b/eslint/babel-eslint-parser/package.json
@@ -34,6 +34,7 @@
     "@babel/plugin-proposal-nullish-coalescing-operator": "^7.0.0",
     "@babel/plugin-proposal-optional-chaining": "^7.0.0",
     "@babel/plugin-proposal-pipeline-operator": "^7.0.0",
+    "@babel/plugin-proposal-private-methods": "^7.7.4",
     "@babel/plugin-syntax-bigint": "^7.7.4",
     "@babel/plugin-syntax-dynamic-import": "^7.0.0",
     "@babel/plugin-syntax-export-default-from": "^7.0.0",
diff --git a/eslint/babel-eslint-parser/src/analyze-scope.js b/eslint/babel-eslint-parser/src/analyze-scope.js
index 24a1b5491c12..ffb9eb95ba82 100644
--- a/eslint/babel-eslint-parser/src/analyze-scope.js
+++ b/eslint/babel-eslint-parser/src/analyze-scope.js
@@ -16,16 +16,16 @@ const flowFlippedAliasKeys = t.FLIPPED_ALIAS_KEYS.Flow.concat([
   "ObjectPattern",
   "RestElement",
 ]);
-const visitorKeysMap = Object.entries(t.VISITOR_KEYS).reduce(function(
-  acc,
-  [key, value],
-) {
-  if (flowFlippedAliasKeys.indexOf(value) === -1) {
-    acc[key] = value;
-  }
-  return acc;
-},
-{});
+
+const visitorKeysMap = Object.entries(t.VISITOR_KEYS).reduce(
+  (acc, [key, value]) => {
+    if (!flowFlippedAliasKeys.includes(value)) {
+      acc[key] = value;
+    }
+    return acc;
+  },
+  {},
+);
 
 const propertyTypes = {
   // loops
@@ -166,6 +166,11 @@ class Referencer extends OriginalReferencer {
     this._visitClassProperty(node);
   }
 
+  // TODO: Update to visit type annotations when TypeScript/Flow support this syntax.
+  ClassPrivateMethod(node) {
+    super.MethodDefinition(node);
+  }
+
   DeclareModule(node) {
     this._visitDeclareX(node);
   }
diff --git a/eslint/babel-eslint-parser/test/babel-eslint-parser.js b/eslint/babel-eslint-parser/test/babel-eslint-parser.js
index fb75112dc966..3924875d38d5 100644
--- a/eslint/babel-eslint-parser/test/babel-eslint-parser.js
+++ b/eslint/babel-eslint-parser/test/babel-eslint-parser.js
@@ -270,7 +270,7 @@ describe("babylon-to-espree", () => {
     assert.strictEqual(babylonAST.tokens[1].type, "Punctuator");
   });
 
-  // Espree doesn't support the private fields yet
+  // Espree doesn't support private fields yet
   it("hash (token)", () => {
     const code = "class A { #x }";
     const babylonAST = parseForESLint(code, {
diff --git a/eslint/babel-eslint-parser/test/fixtures/config/babel.config.js b/eslint/babel-eslint-parser/test/fixtures/config/babel.config.js
index 56a2f07d9707..b84b8d0b3cca 100644
--- a/eslint/babel-eslint-parser/test/fixtures/config/babel.config.js
+++ b/eslint/babel-eslint-parser/test/fixtures/config/babel.config.js
@@ -18,5 +18,6 @@ module.exports = {
     ["@babel/plugin-proposal-decorators", { decoratorsBeforeExport: false }],
     ["@babel/plugin-proposal-pipeline-operator", { proposal: "minimal" }],
     "@babel/plugin-syntax-bigint",
+    "@babel/plugin-proposal-private-methods",
   ],
 };
diff --git a/eslint/babel-eslint-parser/test/non-regression.js b/eslint/babel-eslint-parser/test/non-regression.js
index dca0b489d9ec..418c651d1640 100644
--- a/eslint/babel-eslint-parser/test/non-regression.js
+++ b/eslint/babel-eslint-parser/test/non-regression.js
@@ -1763,27 +1763,77 @@ describe("verify", () => {
     );
   });
 
-  describe("private class properties", () => {
-    it("should not be undefined", () => {
-      verifyAndAssertMessages(
-        `
-            class C {
-              #d = 1;
-            }
-        `,
-        { "no-undef": 1 },
-      );
+  describe("class field declarations", () => {
+    describe("field declarations", () => {
+      it("should not be undefined", () => {
+        verifyAndAssertMessages(
+          `
+              class C {
+                d = 1;
+              }
+          `,
+          { "no-undef": 1 },
+        );
+      });
+
+      it("should not be unused", () => {
+        verifyAndAssertMessages(
+          `
+              export class C {
+                d = 1;
+              }
+          `,
+          { "no-unused-vars": 1 },
+        );
+      });
     });
 
-    it("should not be unused", () => {
-      verifyAndAssertMessages(
-        `
-            export class C {
-              #d = 1;
-            }
-        `,
-        { "no-unused-vars": 1 },
-      );
+    describe("private field declarations", () => {
+      it("should not be undefined", () => {
+        verifyAndAssertMessages(
+          `
+              class C {
+                #d = 1;
+              }
+          `,
+          { "no-undef": 1 },
+        );
+      });
+
+      it("should not be unused", () => {
+        verifyAndAssertMessages(
+          `
+              export class C {
+                #d = 1;
+              }
+          `,
+          { "no-unused-vars": 1 },
+        );
+      });
+    });
+
+    describe("private methods", () => {
+      it("should not be undefined", () => {
+        verifyAndAssertMessages(
+          `
+              class C {
+                #d() {};
+              }
+          `,
+          { "no-undef": 1 },
+        );
+      });
+
+      it("should not be unused", () => {
+        verifyAndAssertMessages(
+          `
+              export class C {
+                #d() {};
+              }
+          `,
+          { "no-unused-vars": 1 },
+        );
+      });
     });
   });
 
@@ -1853,6 +1903,22 @@ describe("verify", () => {
     );
   });
 
+  it("works with classPrivateMethods", () => {
+    verifyAndAssertMessages(
+      `
+        class A { #a(b, c) {} }
+      `,
+    );
+  });
+
+  it("works with arrow function classPrivateProperties", () => {
+    verifyAndAssertMessages(
+      `
+        class A { #a = (a, b) => {}; }
+      `,
+    );
+  });
+
   it("works with optionalCatchBinding", () => {
     verifyAndAssertMessages(
       `