diff --git a/docs/rules/radix.md b/docs/rules/radix.md
index 64466ab6843..da3196c85f0 100644
--- a/docs/rules/radix.md
+++ b/docs/rules/radix.md
@@ -43,6 +43,8 @@ var num = parseInt(someValue);
 
 var num = parseInt("071", "abc");
 
+var num = parseInt("071", 37);
+
 var num = parseInt();
 ```
 
diff --git a/lib/rules/radix.js b/lib/rules/radix.js
index ed3c5cb66b8..6cde887237b 100644
--- a/lib/rules/radix.js
+++ b/lib/rules/radix.js
@@ -18,6 +18,8 @@ const astUtils = require("./utils/ast-utils");
 const MODE_ALWAYS = "always",
     MODE_AS_NEEDED = "as-needed";
 
+const validRadixNumbers = new Set(Array.from({ length: 37 - 2 }, (_, index) => index + 2));
+
 /**
  * Checks whether a given variable is shadowed or not.
  * @param {eslint-scope.Variable} variable A variable to check.
@@ -42,19 +44,20 @@ function isParseIntMethod(node) {
     );
 }
 
+
 /**
  * Checks whether a given node is a valid value of radix or not.
  *
  * The following values are invalid.
  *
- * - A literal except numbers.
+ * - A literal except integers between 2 and 36.
  * - undefined.
  * @param {ASTNode} radix A node of radix to check.
  * @returns {boolean} `true` if the node is valid.
  */
 function isValidRadix(radix) {
     return !(
-        (radix.type === "Literal" && typeof radix.value !== "number") ||
+        (radix.type === "Literal" && !validRadixNumbers.has(radix.value)) ||
         (radix.type === "Identifier" && radix.name === "undefined")
     );
 }
diff --git a/tests/lib/rules/radix.js b/tests/lib/rules/radix.js
index 0acb063a347..18e74f37138 100644
--- a/tests/lib/rules/radix.js
+++ b/tests/lib/rules/radix.js
@@ -107,6 +107,13 @@ ruleTester.run("radix", rule, {
                 type: "CallExpression"
             }]
         },
+        {
+            code: "parseInt(\"10\", 37);",
+            errors: [{
+                message: "Invalid radix parameter.",
+                type: "CallExpression"
+            }]
+        },
         {
             code: "Number.parseInt();",
             errors: [{
@@ -129,6 +136,13 @@ ruleTester.run("radix", rule, {
                 type: "CallExpression"
             }]
         },
+        {
+            code: "Number.parseInt(\"10\", 37);",
+            errors: [{
+                message: "Invalid radix parameter.",
+                type: "CallExpression"
+            }]
+        },
         {
             code: "parseInt(\"10\", 10);",
             options: ["as-needed"],