diff --git a/index.d.ts b/index.d.ts
index cd3dbbd..57d909f 100644
--- a/index.d.ts
+++ b/index.d.ts
@@ -41,7 +41,7 @@ declare const pTimeout: {
 	If you pass in a cancelable promise, specifically a promise with a `.cancel()` method, that method will be called when the `pTimeout` promise times out.
 
 	@param input - Promise to decorate.
-	@param milliseconds - Milliseconds before timing out.
+	@param milliseconds - Milliseconds before timing out. Passing `Infinity` will cause it to never time out.
 	@param fallback - Do something other than rejecting with an error on timeout. You could for example retry.
 	@returns A decorated `input` that times out after `milliseconds` time.
 
diff --git a/index.js b/index.js
index e8ca13d..34d4a4c 100644
--- a/index.js
+++ b/index.js
@@ -14,6 +14,11 @@ const pTimeout = (promise, milliseconds, fallback) => new Promise((resolve, reje
 		throw new TypeError('Expected `milliseconds` to be a positive number');
 	}
 
+	if (milliseconds === Infinity) {
+		resolve(promise);
+		return;
+	}
+
 	const timer = setTimeout(() => {
 		if (typeof fallback === 'function') {
 			try {
diff --git a/readme.md b/readme.md
index 8aec5ab..ad4ab52 100644
--- a/readme.md
+++ b/readme.md
@@ -25,7 +25,8 @@ pTimeout(delayedPromise, 50).then(() => 'foo');
 
 ## API
 
-### pTimeout(input, milliseconds, [message | fallback])
+### pTimeout(input, milliseconds, message?)
+### pTimeout(input, milliseconds, fallback?)
 
 Returns a decorated `input` that times out after `milliseconds` time.
 
@@ -43,6 +44,8 @@ Type: `number`
 
 Milliseconds before timing out.
 
+Passing `Infinity` will cause it to never time out.
+
 #### message
 
 Type: `string` `Error`<br>
@@ -82,8 +85,3 @@ Exposed for instance checking and sub-classing.
 - [p-min-delay](https://github.com/sindresorhus/p-min-delay) - Delay a promise a minimum amount of time
 - [p-retry](https://github.com/sindresorhus/p-retry) - Retry a promise-returning function
 - [More…](https://github.com/sindresorhus/promise-fun)
-
-
-## License
-
-MIT © [Sindre Sorhus](https://sindresorhus.com)
diff --git a/test.js b/test.js
index 0ab8089..4d6ba10 100644
--- a/test.js
+++ b/test.js
@@ -18,6 +18,13 @@ test('throws when milliseconds is negative number', async t => {
 	await t.throwsAsync(pTimeout(delay(50), -1), TypeError);
 });
 
+test('handles milliseconds being `Infinity`', async t => {
+	t.is(
+		await pTimeout(delay(50, {value: fixture}), Infinity),
+		fixture
+	);
+});
+
 test('rejects after timeout', async t => {
 	await t.throwsAsync(pTimeout(delay(200), 50), pTimeout.TimeoutError);
 });