diff --git a/src/stream/stream/max_by.rs b/src/stream/stream/max_by.rs
new file mode 100644
index 00000000..a626b284
--- /dev/null
+++ b/src/stream/stream/max_by.rs
@@ -0,0 +1,57 @@
+use std::cmp::Ordering;
+use std::pin::Pin;
+
+use pin_project_lite::pin_project;
+
+use crate::future::Future;
+use crate::stream::Stream;
+use crate::task::{Context, Poll};
+
+pin_project! {
+    #[doc(hidden)]
+    #[allow(missing_debug_implementations)]
+    pub struct MaxByFuture<S, F, T> {
+        #[pin]
+        stream: S,
+        compare: F,
+        max: Option<T>,
+    }
+}
+
+impl<S, F, T> MaxByFuture<S, F, T> {
+    pub(super) fn new(stream: S, compare: F) -> Self {
+        MaxByFuture {
+            stream,
+            compare,
+            max: None,
+        }
+    }
+}
+
+impl<S, F> Future for MaxByFuture<S, F, S::Item>
+where
+    S: Stream,
+    F: FnMut(&S::Item, &S::Item) -> Ordering,
+{
+    type Output = Option<S::Item>;
+
+    fn poll(self: Pin<&mut Self>, cx: &mut Context<'_>) -> Poll<Self::Output> {
+        let this = self.project();
+        let next = futures_core::ready!(this.stream.poll_next(cx));
+
+        match next {
+            Some(new) => {
+                cx.waker().wake_by_ref();
+                match this.max.take() {
+                    None => *this.max = Some(new),
+                    Some(old) => match (this.compare)(&new, &old) {
+                        Ordering::Greater => *this.max = Some(new),
+                        _ => *this.max = Some(old),
+                    },
+                }
+                Poll::Pending
+            }
+            None => Poll::Ready(this.max.take()),
+        }
+    }
+}
diff --git a/src/stream/stream/mod.rs b/src/stream/stream/mod.rs
index aadd058b..e8190387 100644
--- a/src/stream/stream/mod.rs
+++ b/src/stream/stream/mod.rs
@@ -40,6 +40,7 @@ mod last;
 mod le;
 mod lt;
 mod map;
+mod max_by;
 mod min_by;
 mod min_by_key;
 mod next;
@@ -69,6 +70,7 @@ use gt::GtFuture;
 use last::LastFuture;
 use le::LeFuture;
 use lt::LtFuture;
+use max_by::MaxByFuture;
 use min_by::MinByFuture;
 use min_by_key::MinByKeyFuture;
 use next::NextFuture;
@@ -758,6 +760,45 @@ extension_trait! {
             MinByFuture::new(self, compare)
         }
 
+         #[doc = r#"
+            Returns the element that gives the maximum value with respect to the
+            specified comparison function. If several elements are equally maximum,
+            the first element is returned. If the stream is empty, `None` is returned.
+
+            # Examples
+
+            ```
+            # fn main() { async_std::task::block_on(async {
+            #
+            use std::collections::VecDeque;
+
+            use async_std::prelude::*;
+
+            let s: VecDeque<usize> = vec![1, 2, 3].into_iter().collect();
+
+            let max = s.clone().max_by(|x, y| x.cmp(y)).await;
+            assert_eq!(max, Some(3));
+
+            let max = s.max_by(|x, y| y.cmp(x)).await;
+            assert_eq!(max, Some(1));
+
+            let max = VecDeque::<usize>::new().max_by(|x, y| x.cmp(y)).await;
+            assert_eq!(max, None);
+            #
+            # }) }
+            ```
+        "#]
+        fn max_by<F>(
+            self,
+            compare: F,
+        ) -> impl Future<Output = Option<Self::Item>> [MaxByFuture<Self, F, Self::Item>]
+        where
+            Self: Sized,
+            F: FnMut(&Self::Item, &Self::Item) -> Ordering,
+        {
+            MaxByFuture::new(self, compare)
+        }
+
         #[doc = r#"
             Returns the nth element of the stream.