diff --git a/http2/transport.go b/http2/transport.go
index e78804b..5a179b6 100644
--- a/http2/transport.go
+++ b/http2/transport.go
@@ -16,6 +16,7 @@
 	"errors"
 	"fmt"
 	"io"
+	"io/fs"
 	"log"
 	"math"
 	mathrand "math/rand"
@@ -2985,7 +2986,11 @@
 }
 
 func (gz *gzipReader) Close() error {
-	return gz.body.Close()
+	if err := gz.body.Close(); err != nil {
+		return err
+	}
+	gz.zerr = fs.ErrClosed
+	return nil
 }
 
 type errorReader struct{ err error }
diff --git a/http2/transport_test.go b/http2/transport_test.go
index 67afb57..c738911 100644
--- a/http2/transport_test.go
+++ b/http2/transport_test.go
@@ -7,6 +7,7 @@
 import (
 	"bufio"
 	"bytes"
+	"compress/gzip"
 	"context"
 	"crypto/tls"
 	"encoding/hex"
@@ -14,6 +15,7 @@
 	"flag"
 	"fmt"
 	"io"
+	"io/fs"
 	"io/ioutil"
 	"log"
 	"math/rand"
@@ -2503,6 +2505,28 @@
 	}
 }
 
+func TestGzipReader_ReadAfterClose(t *testing.T) {
+	body := bytes.Buffer{}
+	w := gzip.NewWriter(&body)
+	w.Write([]byte("012345679"))
+	w.Close()
+	gz := &gzipReader{
+		body: ioutil.NopCloser(&body),
+	}
+	var buf [1]byte
+	n, err := gz.Read(buf[:])
+	if n != 1 || err != nil {
+		t.Fatalf("first Read = %v, %v; want 1, nil", n, err)
+	}
+	if err := gz.Close(); err != nil {
+		t.Fatalf("gz Close error: %v", err)
+	}
+	n, err = gz.Read(buf[:])
+	if n != 0 || err != fs.ErrClosed {
+		t.Fatalf("Read after close = %v, %v; want 0, fs.ErrClosed", n, err)
+	}
+}
+
 func TestTransportNewTLSConfig(t *testing.T) {
 	tests := [...]struct {
 		conf *tls.Config