diff --git a/Cargo.toml b/Cargo.toml
index 71e6636b..213b14a7 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -125,6 +125,11 @@ name = "gateway"
 path = "examples/gateway.rs"
 required-features = ["full"]
 
+[[example]]
+name = "graceful_shutdown"
+path = "examples/graceful_shutdown.rs"
+required-features = ["full"]
+
 [[example]]
 name = "hello"
 path = "examples/hello.rs"
diff --git a/examples/README.md b/examples/README.md
index 2511c4be..5010b39c 100644
--- a/examples/README.md
+++ b/examples/README.md
@@ -42,6 +42,8 @@ futures-util = { version = "0.3", default-features = false, features = ["alloc"]
 
 * [`gateway`](gateway.rs) - A server gateway (reverse proxy) that proxies to the `hello` service above.
 
+* [`graceful_shutdown`](graceful_shutdown.rs) - A server that has a timeout for incoming connections and does graceful connection shutdown.
+
 * [`http_proxy`](http_proxy.rs) - A simple HTTP(S) proxy that handle and upgrade `CONNECT` requests and then proxy data between client and remote server.
 
 * [`multi_server`](multi_server.rs) - A server that listens to two different ports, a different `Service` per port.
diff --git a/examples/graceful_shutdown.rs b/examples/graceful_shutdown.rs
new file mode 100644
index 00000000..47fbb8da
--- /dev/null
+++ b/examples/graceful_shutdown.rs
@@ -0,0 +1,95 @@
+#![deny(warnings)]
+
+use std::convert::Infallible;
+use std::net::SocketAddr;
+use std::time::Duration;
+
+use bytes::Bytes;
+use http_body_util::Full;
+use hyper::server::conn::http1;
+use hyper::service::service_fn;
+use hyper::{Request, Response};
+use tokio::net::TcpListener;
+use tokio::pin;
+
+#[path = "../benches/support/mod.rs"]
+mod support;
+use support::TokioIo;
+
+// An async function that consumes a request, does nothing with it and returns a
+// response.
+async fn hello(_: Request<hyper::body::Incoming>) -> Result<Response<Full<Bytes>>, Infallible> {
+    // Sleep for 6 seconds to simulate long processing.
+    // This is longer than the initial 5 second connection timeout,
+    // but within the 2 second graceful shutdown timeout.
+    println!("in hello before sleep");
+    tokio::time::sleep(Duration::from_secs(6)).await;
+    println!("in hello after sleep");
+    Ok(Response::new(Full::new(Bytes::from("Hello World!"))))
+}
+
+#[tokio::main]
+pub async fn main() -> Result<(), Box<dyn std::error::Error + Send + Sync>> {
+    pretty_env_logger::init();
+
+    // This address is localhost
+    let addr: SocketAddr = ([127, 0, 0, 1], 3000).into();
+
+    // Use a 5 second timeout for incoming connections to the server.
+    // If a request is in progress when the 5 second timeout elapses,
+    // use a 2 second timeout for processing the final request and graceful shutdown.
+    let connection_timeouts = vec![Duration::from_secs(5), Duration::from_secs(2)];
+
+    // Bind to the port and listen for incoming TCP connections
+    let listener = TcpListener::bind(addr).await?;
+    println!("Listening on http://{}", addr);
+    loop {
+        // When an incoming TCP connection is received grab a TCP stream for
+        // client<->server communication.
+        let (tcp, remote_address) = listener.accept().await?;
+
+        // Use an adapter to access something implementing `tokio::io` traits as if they implement
+        // `hyper::rt` IO traits.
+        let io = TokioIo::new(tcp);
+
+        // Print the remote address connecting to our server.
+        println!("accepted connection from {:?}", remote_address);
+
+        // Clone the connection_timeouts so they can be passed to the new task.
+        let connection_timeouts_clone = connection_timeouts.clone();
+
+        // Spin up a new task in Tokio so we can continue to listen for new TCP connection on the
+        // current task without waiting for the processing of the HTTP1 connection we just received
+        // to finish
+        tokio::task::spawn(async move {
+            // Pin the connection object so we can use tokio::select! below.
+            let conn = http1::Builder::new().serve_connection(io, service_fn(hello));
+            pin!(conn);
+
+            // Iterate the timeouts.  Use tokio::select! to wait on the
+            // result of polling the connection itself,
+            // and also on tokio::time::sleep for the current timeout duration.
+            for (iter, sleep_duration) in connection_timeouts_clone.iter().enumerate() {
+                println!("iter = {} sleep_duration = {:?}", iter, sleep_duration);
+                tokio::select! {
+                    res = conn.as_mut() => {
+                        // Polling the connection returned a result.
+                        // In this case print either the successful or error result for the connection
+                        // and break out of the loop.
+                        match res {
+                            Ok(()) => println!("after polling conn, no error"),
+                            Err(e) =>  println!("error serving connection: {:?}", e),
+                        };
+                        break;
+                    }
+                    _ = tokio::time::sleep(*sleep_duration) => {
+                        // tokio::time::sleep returned a result.
+                        // Call graceful_shutdown on the connection and continue the loop.
+                        println!("iter = {} got timeout_interval, calling conn.graceful_shutdown", iter);
+                        conn.as_mut().graceful_shutdown();
+                    }
+                }
+            }
+        });
+    }
+}