diff --git a/lib/rules/no-constant-condition.js b/lib/rules/no-constant-condition.js
index 39c2928eed3..fb36207ebbb 100644
--- a/lib/rules/no-constant-condition.js
+++ b/lib/rules/no-constant-condition.js
@@ -5,6 +5,13 @@
 
 "use strict";
 
+//------------------------------------------------------------------------------
+// Helpers
+//------------------------------------------------------------------------------
+
+const EQUALITY_OPERATORS = ["===", "!==", "==", "!="];
+const RELATIONAL_OPERATORS = [">", "<", ">=", "<=", "in", "instanceof"];
+
 //------------------------------------------------------------------------------
 // Rule Definition
 //------------------------------------------------------------------------------
@@ -110,7 +117,18 @@ module.exports = {
                     const isRightShortCircuit = (isRightConstant && isLogicalIdentity(node.right, node.operator));
 
                     return (isLeftConstant && isRightConstant) ||
-                        (node.operator === "||" && isRightConstant && node.right.value) || // in the case of an "OR", we need to know if the right constant value is truthy
+                        (
+
+                            // in the case of an "OR", we need to know if the right constant value is truthy
+                            node.operator === "||" &&
+                            isRightConstant &&
+                            node.right.value &&
+                            (
+                                !node.parent ||
+                                node.parent.type !== "BinaryExpression" ||
+                                !(EQUALITY_OPERATORS.includes(node.parent.operator) || RELATIONAL_OPERATORS.includes(node.parent.operator))
+                            )
+                        ) ||
                         isLeftShortCircuit ||
                         isRightShortCircuit;
                 }
diff --git a/tests/lib/rules/no-constant-condition.js b/tests/lib/rules/no-constant-condition.js
index c89f9080d6e..e27e3b390b7 100644
--- a/tests/lib/rules/no-constant-condition.js
+++ b/tests/lib/rules/no-constant-condition.js
@@ -61,6 +61,18 @@ ruleTester.run("no-constant-condition", rule, {
         "if(a && 'str'){}",
         "if('str' || abc==='str'){}",
 
+        // #11306
+        "if ((foo || 'bar') === 'baz') {}",
+        "if ((foo || 'bar') !== 'baz') {}",
+        "if ((foo || 'bar') == 'baz') {}",
+        "if ((foo || 'bar') != 'baz') {}",
+        "if ((foo || 233) > 666) {}",
+        "if ((foo || 233) < 666) {}",
+        "if ((foo || 233) >= 666) {}",
+        "if ((foo || 233) <= 666) {}",
+        "if ((key || 'k') in obj) {}",
+        "if ((foo || {}) instanceof obj) {}",
+
         // { checkLoops: false }
         { code: "while(true);", options: [{ checkLoops: false }] },
         { code: "for(;true;);", options: [{ checkLoops: false }] },