diff --git a/src/bufio/bufio.go b/src/bufio/bufio.go
index 7cf395c6e6..d2ccc74f52 100644
--- a/src/bufio/bufio.go
+++ b/src/bufio/bufio.go
@@ -124,14 +124,16 @@ func (b *Reader) Peek(n int) ([]byte, error) {
 	if n < 0 {
 		return nil, ErrNegativeCount
 	}
-	if n > len(b.buf) {
-		return nil, ErrBufferFull
-	}
-	// 0 <= n <= len(b.buf)
-	for b.w-b.r < n && b.err == nil {
+
+	for b.w-b.r < n && b.w-b.r < len(b.buf) && b.err == nil {
 		b.fill() // b.w-b.r < len(b.buf) => buffer is not full
 	}
 
+	if n > len(b.buf) {
+		return b.buf[b.r:b.w], ErrBufferFull
+	}
+
+	// 0 <= n <= len(b.buf)
 	var err error
 	if avail := b.w - b.r; avail < n {
 		// not enough data in buffer
diff --git a/src/bufio/bufio_test.go b/src/bufio/bufio_test.go
index 666c44e15a..d769a6aaa9 100644
--- a/src/bufio/bufio_test.go
+++ b/src/bufio/bufio_test.go
@@ -673,8 +673,8 @@ func TestPeek(t *testing.T) {
 	if _, err := buf.Peek(-1); err != ErrNegativeCount {
 		t.Fatalf("want ErrNegativeCount got %v", err)
 	}
-	if _, err := buf.Peek(32); err != ErrBufferFull {
-		t.Fatalf("want ErrBufFull got %v", err)
+	if s, err := buf.Peek(32); string(s) != "abcdefghijklmnop" || err != ErrBufferFull {
+		t.Fatalf("want %q, ErrBufFull got %q, err=%v", "abcdefghijklmnop", string(s), err)
 	}
 	if _, err := buf.Read(p[0:3]); string(p[0:3]) != "abc" || err != nil {
 		t.Fatalf("want %q got %q, err=%v", "abc", string(p[0:3]), err)