diff --git a/docs/rules/no-new-func.md b/docs/rules/no-new-func.md
index 16ac00c6acb..7bdfc9ec732 100644
--- a/docs/rules/no-new-func.md
+++ b/docs/rules/no-new-func.md
@@ -1,12 +1,16 @@
 # Disallow Function Constructor (no-new-func)
 
-It's possible to create functions in JavaScript using the `Function` constructor, such as:
+It's possible to create functions in JavaScript from strings at runtime using the `Function` constructor, such as:
 
 ```js
 var x = new Function("a", "b", "return a + b");
+var x = Function("a", "b", "return a + b");
+var x = Function.call(null, "a", "b", "return a + b");
+var x = Function.apply(null, ["a", "b", "return a + b"]);
+var x = Function.bind(null, "a", "b", "return a + b")();
 ```
 
-This is considered by many to be a bad practice due to the difficulty in debugging and reading these types of functions.
+This is considered by many to be a bad practice due to the difficulty in debugging and reading these types of functions. In addition, Content-Security-Policy (CSP) directives may disallow the use of eval() and similar methods for creating code from strings.
 
 ## Rule Details
 
@@ -19,6 +23,10 @@ Examples of **incorrect** code for this rule:
 
 var x = new Function("a", "b", "return a + b");
 var x = Function("a", "b", "return a + b");
+var x = Function.call(null, "a", "b", "return a + b");
+var x = Function.apply(null, ["a", "b", "return a + b"]);
+var x = Function.bind(null, "a", "b", "return a + b")();
+var f = Function.bind(null, "a", "b", "return a + b"); // assuming that the result of Function.bind(...) will be eventually called.
 ```
 
 Examples of **correct** code for this rule:
diff --git a/lib/rules/no-new-func.js b/lib/rules/no-new-func.js
index eebc68c80c2..ddf61024dac 100644
--- a/lib/rules/no-new-func.js
+++ b/lib/rules/no-new-func.js
@@ -5,6 +5,18 @@
 
 "use strict";
 
+//------------------------------------------------------------------------------
+// Requirements
+//------------------------------------------------------------------------------
+
+const astUtils = require("./utils/ast-utils");
+
+//------------------------------------------------------------------------------
+// Helpers
+//------------------------------------------------------------------------------
+
+const callMethods = new Set(["apply", "bind", "call"]);
+
 //------------------------------------------------------------------------------
 // Rule Definition
 //------------------------------------------------------------------------------
@@ -37,14 +49,30 @@ module.exports = {
                     variable.references.forEach(ref => {
                         const node = ref.identifier;
                         const { parent } = node;
+                        let evalNode;
+
+                        if (parent) {
+                            if (node === parent.callee && (
+                                parent.type === "NewExpression" ||
+                                parent.type === "CallExpression"
+                            )) {
+                                evalNode = parent;
+                            } else if (
+                                parent.type === "MemberExpression" &&
+                                node === parent.object &&
+                                callMethods.has(astUtils.getStaticPropertyName(parent))
+                            ) {
+                                const maybeCallee = parent.parent.type === "ChainExpression" ? parent.parent : parent;
+
+                                if (maybeCallee.parent.type === "CallExpression" && maybeCallee.parent.callee === maybeCallee) {
+                                    evalNode = maybeCallee.parent;
+                                }
+                            }
+                        }
 
-                        if (
-                            parent &&
-                            (parent.type === "NewExpression" || parent.type === "CallExpression") &&
-                            node === parent.callee
-                        ) {
+                        if (evalNode) {
                             context.report({
-                                node: parent,
+                                node: evalNode,
                                 messageId: "noFunctionConstructor"
                             });
                         }
diff --git a/tests/lib/rules/no-new-func.js b/tests/lib/rules/no-new-func.js
index aa0542090e2..1ac02d97465 100644
--- a/tests/lib/rules/no-new-func.js
+++ b/tests/lib/rules/no-new-func.js
@@ -38,7 +38,11 @@ ruleTester.run("no-new-func", rule, {
         "var fn = function () { function Function() {}; Function() }",
         "var x = function Function() { Function(); }",
         "call(Function)",
-        "new Class(Function)"
+        "new Class(Function)",
+        "foo[Function]()",
+        "foo(Function.bind)",
+        "Function.toString()",
+        "Function[call]()"
     ],
     invalid: [
         {
@@ -55,6 +59,49 @@ ruleTester.run("no-new-func", rule, {
                 type: "CallExpression"
             }]
         },
+        {
+            code: "var a = Function.call(null, \"b\", \"c\", \"return b+c\");",
+            errors: [{
+                messageId: "noFunctionConstructor",
+                type: "CallExpression"
+            }]
+        },
+        {
+            code: "var a = Function.apply(null, [\"b\", \"c\", \"return b+c\"]);",
+            errors: [{
+                messageId: "noFunctionConstructor",
+                type: "CallExpression"
+            }]
+        },
+        {
+            code: "var a = Function.bind(null, \"b\", \"c\", \"return b+c\")();",
+            errors: [{
+                messageId: "noFunctionConstructor",
+                type: "CallExpression"
+            }]
+        },
+        {
+            code: "var a = Function.bind(null, \"b\", \"c\", \"return b+c\");",
+            errors: [{
+                messageId: "noFunctionConstructor",
+                type: "CallExpression"
+            }]
+        },
+        {
+            code: "var a = Function[\"call\"](null, \"b\", \"c\", \"return b+c\");",
+            errors: [{
+                messageId: "noFunctionConstructor",
+                type: "CallExpression"
+            }]
+        },
+        {
+            code: "var a = (Function?.call)(null, \"b\", \"c\", \"return b+c\");",
+            parserOptions: { ecmaVersion: 2021 },
+            errors: [{
+                messageId: "noFunctionConstructor",
+                type: "CallExpression"
+            }]
+        },
         {
             code: "const fn = () => { class Function {} }; new Function('', '')",
             parserOptions: {