diff --git a/library/std/src/io/buffered/bufreader.rs b/library/std/src/io/buffered/bufreader.rs
index 035afbb8368b4..7dcca2707ba10 100644
--- a/library/std/src/io/buffered/bufreader.rs
+++ b/library/std/src/io/buffered/bufreader.rs
@@ -99,7 +99,10 @@ impl<R: Read> BufReader<R> {
 impl<R: Read + ?Sized> BufReader<R> {
     /// Attempt to look ahead `n` bytes.
     ///
-    /// `n` must be less than `capacity`.
+    /// `n` must be less than or equal to `capacity`.
+    ///
+    /// the returned slice may be less than `n` bytes long if
+    /// end of file is reached.
     ///
     /// ## Examples
     ///
@@ -117,6 +120,7 @@ impl<R: Read + ?Sized> BufReader<R> {
     /// let mut s = String::new();
     /// rdr.read_to_string(&mut s).unwrap();
     /// assert_eq!(&s, "hello");
+    /// assert_eq!(rdr.peek(1).unwrap().len(), 0);
     /// ```
     #[unstable(feature = "bufreader_peek", issue = "128405")]
     pub fn peek(&mut self, n: usize) -> io::Result<&[u8]> {
@@ -125,7 +129,11 @@ impl<R: Read + ?Sized> BufReader<R> {
             if self.buf.pos() > 0 {
                 self.buf.backshift();
             }
-            self.buf.read_more(&mut self.inner)?;
+            let new = self.buf.read_more(&mut self.inner)?;
+            if new == 0 {
+                // end of file, no more bytes to read
+                return Ok(&self.buf.buffer()[..]);
+            }
             debug_assert_eq!(self.buf.pos(), 0);
         }
         Ok(&self.buf.buffer()[..n])
diff --git a/library/std/src/io/buffered/bufreader/buffer.rs b/library/std/src/io/buffered/bufreader/buffer.rs
index ccd67fafb45b4..1bf84d8bef312 100644
--- a/library/std/src/io/buffered/bufreader/buffer.rs
+++ b/library/std/src/io/buffered/bufreader/buffer.rs
@@ -98,7 +98,7 @@ impl Buffer {
     }
 
     /// Read more bytes into the buffer without discarding any of its contents
-    pub fn read_more(&mut self, mut reader: impl Read) -> io::Result<()> {
+    pub fn read_more(&mut self, mut reader: impl Read) -> io::Result<usize> {
         let mut buf = BorrowedBuf::from(&mut self.buf[self.pos..]);
         let old_init = self.initialized - self.pos;
         unsafe {
@@ -107,7 +107,7 @@ impl Buffer {
         reader.read_buf(buf.unfilled())?;
         self.filled += buf.len();
         self.initialized += buf.init_len() - old_init;
-        Ok(())
+        Ok(buf.len())
     }
 
     /// Remove bytes that have already been read from the buffer.