diff --git a/lib/_stream_readable.js b/lib/_stream_readable.js
index cfa36731e3d661..24f9b6bca83a9a 100644
--- a/lib/_stream_readable.js
+++ b/lib/_stream_readable.js
@@ -420,6 +420,11 @@ Readable.prototype.read = function(n) {
     n = parseInt(n, 10);
   }
   const state = this._readableState;
+
+  if (state.destroyed) {
+    return;
+  }
+
   const nOrig = n;
 
   // If we're asking for more than the current hwm, then raise the hwm.
@@ -643,7 +648,7 @@ function maybeReadMore_(stream, state) {
   //   called push() with new data. In this case we skip performing more
   //   read()s. The execution ends in this method again after the _read() ends
   //   up calling push() with more data.
-  while (!state.reading && !state.ended &&
+  while (!state.reading && !state.ended && !state.destroyed &&
          (state.length < state.highWaterMark ||
           (state.flowing && state.length === 0))) {
     const len = state.length;
@@ -976,6 +981,12 @@ function resume(stream, state) {
 
 function resume_(stream, state) {
   debug('resume', state.reading);
+
+  if (state.destroyed) {
+    state.resumeScheduled = false;
+    return;
+  }
+
   if (!state.reading) {
     stream.read(0);
   }
diff --git a/test/parallel/test-stream-readable-destroy.js b/test/parallel/test-stream-readable-destroy.js
index 05e7dd464ddca0..7687ea90cc82d8 100644
--- a/test/parallel/test-stream-readable-destroy.js
+++ b/test/parallel/test-stream-readable-destroy.js
@@ -189,3 +189,12 @@ const assert = require('assert');
   read.push('hi');
   read.on('data', common.mustNotCall());
 }
+
+{
+  const read = new Readable({
+    read: common.mustNotCall(function() {})
+  });
+  read.destroy();
+  assert.strictEqual(read.destroyed, true);
+  read.read();
+}
diff --git a/test/parallel/test-stream-transform-destroy.js b/test/parallel/test-stream-transform-destroy.js
index c594d9989ae4de..f6c4419aadf1a5 100644
--- a/test/parallel/test-stream-transform-destroy.js
+++ b/test/parallel/test-stream-transform-destroy.js
@@ -91,35 +91,6 @@ const assert = require('assert');
   transform.destroy();
 }
 
-{
-  const transform = new Transform({
-    transform(chunk, enc, cb) {}
-  });
-  transform.resume();
-
-  transform._destroy = common.mustCall(function(err, cb) {
-    assert.strictEqual(err, null);
-    process.nextTick(() => {
-      this.push(null);
-      this.end();
-      cb();
-    });
-  }, 1);
-
-  const fail = common.mustNotCall('no event');
-
-  transform.on('finish', fail);
-  transform.on('end', fail);
-  transform.on('close', common.mustCall());
-
-  transform.destroy();
-
-  transform.removeListener('end', fail);
-  transform.removeListener('finish', fail);
-  transform.on('end', common.mustCall());
-  transform.on('finish', common.mustCall());
-}
-
 {
   const transform = new Transform({
     transform(chunk, enc, cb) {}