diff --git a/lib/_http_server.js b/lib/_http_server.js
index 0b4077bf07367a..2df4260411fd31 100644
--- a/lib/_http_server.js
+++ b/lib/_http_server.js
@@ -681,6 +681,7 @@ Server.prototype.closeIdleConnections = function closeIdleConnections() {
   }
 
   const connections = this[kConnections].idle();
+  const allConnections = this[kConnections].all();
 
   for (let i = 0, l = connections.length; i < l; i++) {
     if (connections[i].socket._httpMessage && !connections[i].socket._httpMessage.finished) {
@@ -689,6 +690,12 @@ Server.prototype.closeIdleConnections = function closeIdleConnections() {
 
     connections[i].socket.destroy();
   }
+
+  for (let i = 0, l = allConnections.length; i < l; i++) {
+    if (allConnections[i].socket.bytesRead === 0) {
+      allConnections[i].socket.destroy();
+    }
+  }
 };
 
 Server.prototype.setTimeout = function setTimeout(msecs, callback) {
diff --git a/test/parallel/test-http-server-close-idle-connections-pre-request.js b/test/parallel/test-http-server-close-idle-connections-pre-request.js
new file mode 100644
index 00000000000000..a9142b17348969
--- /dev/null
+++ b/test/parallel/test-http-server-close-idle-connections-pre-request.js
@@ -0,0 +1,23 @@
+'use strict';
+
+const common = require('../common');
+
+const { createServer } = require('http');
+const { createConnection } = require('net');
+
+const server = createServer(common.mustNotCall());
+
+server.listen(0, '127.0.0.1', common.mustCall(() => {
+  const port = server.address().port;
+  server.once('connection', common.mustCall(() => {
+    server.close(common.mustCall());
+    server.closeIdleConnections();
+    setTimeout(common.mustNotCall(), common.platformTimeout(1000)).unref();
+  }));
+
+  const socket = createConnection(port, '127.0.0.1');
+
+  socket.on('connect', common.mustCall());
+  socket.on('close', common.mustCall());
+  socket.on('error', () => {});
+}));