diff --git a/lib/internal/streams/async_iterator.js b/lib/internal/streams/async_iterator.js
index 25b393d21f1fcb..90960f5a3842e3 100644
--- a/lib/internal/streams/async_iterator.js
+++ b/lib/internal/streams/async_iterator.js
@@ -127,7 +127,10 @@ const createReadableStreamAsyncIterator = (stream) => {
     [kLastResolve]: { value: null, writable: true },
     [kLastReject]: { value: null, writable: true },
     [kError]: { value: null, writable: true },
-    [kEnded]: { value: false, writable: true },
+    [kEnded]: {
+      value: stream._readableState.endEmitted,
+      writable: true
+    },
     [kLastPromise]: { value: null, writable: true },
     // the function passed to new Promise
     // is cached so we avoid allocating a new
@@ -150,7 +153,7 @@ const createReadableStreamAsyncIterator = (stream) => {
   });
 
   finished(stream, (err) => {
-    if (err) {
+    if (err && err.code !== 'ERR_STREAM_PREMATURE_CLOSE') {
       const reject = iterator[kLastReject];
       // reject if we are waiting for data in the Promise
       // returned by next() and store the error
diff --git a/test/parallel/test-stream-readable-async-iterators.js b/test/parallel/test-stream-readable-async-iterators.js
index ec558955c6ed18..83540de9defea3 100644
--- a/test/parallel/test-stream-readable-async-iterators.js
+++ b/test/parallel/test-stream-readable-async-iterators.js
@@ -335,11 +335,8 @@ async function tests() {
 
     readable.destroy();
 
-    try {
-      await readable[Symbol.asyncIterator]().next();
-    } catch (e) {
-      assert.strictEqual(e.code, 'ERR_STREAM_PREMATURE_CLOSE');
-    }
+    const { done } = await readable[Symbol.asyncIterator]().next();
+    assert.strictEqual(done, true);
   })();
 
   await (async function() {
@@ -362,6 +359,40 @@ async function tests() {
       assert.strictEqual(e, err);
     }
   })();
+
+  await (async () => {
+    console.log('iterating on an ended stream completes');
+    const r = new Readable({
+      objectMode: true,
+      read() {
+        this.push('asdf');
+        this.push('hehe');
+        this.push(null);
+      }
+    });
+    // eslint-disable-next-line no-unused-vars
+    for await (const a of r) {
+    }
+    // eslint-disable-next-line no-unused-vars
+    for await (const b of r) {
+    }
+  })();
+
+  await (async () => {
+    console.log('destroy mid-stream does not error');
+    const r = new Readable({
+      objectMode: true,
+      read() {
+        this.push('asdf');
+        this.push('hehe');
+      }
+    });
+
+    // eslint-disable-next-line no-unused-vars
+    for await (const a of r) {
+      r.destroy(null);
+    }
+  })();
 }
 
 // to avoid missing some tests if a promise does not resolve