diff --git a/transport/http2_client_transport.go b/transport/http2_client.go
similarity index 99%
rename from transport/http2_client_transport.go
rename to transport/http2_client.go
index f2147509..9b2840a1 100644
--- a/transport/http2_client_transport.go
+++ b/transport/http2_client.go
@@ -35,6 +35,7 @@ package transport
 
 import (
 	"bytes"
+	"errors"
 	"io"
 	"log"
 	"math"
@@ -315,6 +316,10 @@ func (t *http2Client) CloseStream(s *Stream, err error) {
 // accessed any more.
 func (t *http2Client) Close() (err error) {
 	t.mu.Lock()
+	if t.state == closing {
+		t.mu.Unlock()
+		return errors.New("transport: Close() was already called")
+	}
 	t.state = closing
 	t.mu.Unlock()
 	close(t.shutdownChan)
diff --git a/transport/http2_server_transport.go b/transport/http2_server.go
similarity index 99%
rename from transport/http2_server_transport.go
rename to transport/http2_server.go
index 633e3f51..53a09bf3 100644
--- a/transport/http2_server_transport.go
+++ b/transport/http2_server.go
@@ -79,7 +79,7 @@ type http2Server struct {
 	// sendQuotaPool provides flow control to outbound message.
 	sendQuotaPool *quotaPool
 
-	mu            sync.Mutex
+	mu            sync.Mutex // guard the following
 	state         transportState
 	activeStreams map[uint32]*Stream
 	// Inbound quota for flow control
@@ -570,7 +570,7 @@ func (t *http2Server) Close() (err error) {
 	t.mu.Lock()
 	if t.state == closing {
 		t.mu.Unlock()
-		return
+		return errors.New("transport: Close() was already called")
 	}
 	t.state = closing
 	streams := t.activeStreams
diff --git a/transport/transport.go b/transport/transport.go
index 2cd211e6..406d581f 100644
--- a/transport/transport.go
+++ b/transport/transport.go
@@ -186,7 +186,7 @@ type Stream struct {
 	// The key-value map of trailer metadata.
 	trailer metadata.MD
 
-	mu sync.RWMutex
+	mu sync.RWMutex // guard the following
 	// headerOK becomes true from the first header is about to send.
 	headerOk bool
 	state    streamState
diff --git a/transport/transport_test.go b/transport/transport_test.go
index bac71160..e768f7a5 100644
--- a/transport/transport_test.go
+++ b/transport/transport_test.go
@@ -158,12 +158,12 @@ func (s *server) Wait(t *testing.T, timeout time.Duration) {
 }
 
 func (s *server) Close() {
+	// Keep consistent with closeServer().
 	s.lis.Close()
 	s.mu.Lock()
 	for c := range s.conns {
 		c.Close()
 	}
-	s.conns = nil
 	s.mu.Unlock()
 }
 
@@ -227,8 +227,8 @@ func TestClientSendAndReceive(t *testing.T) {
 	if recvErr != io.EOF {
 		t.Fatalf("Error: %v; want <EOF>", recvErr)
 	}
-	ct.Close()
-	server.Close()
+	closeClient(ct, t)
+	closeServer(server, t)
 }
 
 func TestClientErrorNotify(t *testing.T) {
@@ -245,10 +245,10 @@ func TestClientErrorNotify(t *testing.T) {
 		t.Fatalf("wrong stream id: %d", s.id)
 	}
 	// Tear down the server.
-	go server.Close()
+	go closeServer(server, t)
 	// ct.reader should detect the error and activate ct.Error().
 	<-ct.Error()
-	ct.Close()
+	closeClient(ct, t)
 }
 
 func performOneRPC(ct ClientTransport) {
@@ -281,11 +281,11 @@ func TestClientMix(t *testing.T) {
 	s, ct := setUp(t, true, 0, math.MaxUint32, false)
 	go func(s *server) {
 		time.Sleep(5 * time.Second)
-		s.Close()
+		closeServer(s, t)
 	}(s)
-	go func(t ClientTransport) {
+	go func(ct ClientTransport) {
 		<-ct.Error()
-		ct.Close()
+		closeClient(ct, t)
 	}(ct)
 	for i := 0; i < 1000; i++ {
 		time.Sleep(10 * time.Millisecond)
@@ -296,8 +296,8 @@ func TestClientMix(t *testing.T) {
 func TestExceedMaxStreamsLimit(t *testing.T) {
 	server, ct := setUp(t, true, 0, 1, false)
 	defer func() {
-		ct.Close()
-		server.Close()
+		closeClient(ct, t)
+		closeServer(server, t)
 	}()
 	callHdr := &CallHdr{
 		Host:   "localhost",
@@ -371,8 +371,8 @@ func TestLargeMessage(t *testing.T) {
 		}()
 	}
 	wg.Wait()
-	ct.Close()
-	server.Close()
+	closeClient(ct, t)
+	closeServer(server, t)
 }
 
 func TestLargeMessageSuspension(t *testing.T) {
@@ -393,8 +393,8 @@ func TestLargeMessageSuspension(t *testing.T) {
 	if err == nil || err != expectedErr {
 		t.Fatalf("Write got %v, want %v", err, expectedErr)
 	}
-	ct.Close()
-	server.Close()
+	closeClient(ct, t)
+	closeServer(server, t)
 }
 
 func TestStreamContext(t *testing.T) {
@@ -405,3 +405,53 @@ func TestStreamContext(t *testing.T) {
 		t.Fatalf("GetStreamFromContext(%v) = %v, %t, want: %v, true", ctx, *s, ok, expectedStream)
 	}
 }
+
+// closeClient shuts down the ClientTransport and reports any errors to the
+// test framework and terminates the current test case.
+func closeClient(ct ClientTransport, t *testing.T) {
+	if err := ct.Close(); err != nil {
+		t.Fatalf("ct.Close() = %v, want <nil>", err)
+	}
+}
+
+// closeServerWithErr shuts down the testing server, closing the associated
+// transports.  It returns the first error it encounters, if any.
+func closeServerWithErr(s *server) error {
+	// Keep consistent with s.Close().
+	s.lis.Close()
+	s.mu.Lock()
+	defer s.mu.Unlock()
+	for c := range s.conns {
+		if err := c.Close(); err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
+// closeServer shuts down the and testing server, closing the associated
+// transport.  It reports any errors to the test framework and terminates the
+// current test case.
+func closeServer(s *server, t *testing.T) {
+	if err := closeServerWithErr(s); err != nil {
+		t.Fatalf("server.Close() = %v, want <nil>", err)
+	}
+}
+
+func TestClientServerDuplicatedClose(t *testing.T) {
+	server, ct := setUp(t, true, 0, math.MaxUint32, false)
+	if err := ct.Close(); err != nil {
+		t.Fatalf("ct.Close() = %v, want <nil>", err)
+	}
+	if err := ct.Close(); err == nil {
+		// Duplicated closes should gracefully issue an error.
+		t.Fatalf("ct.Close() = <nil>, want non-nil")
+	}
+	if err := closeServerWithErr(server); err != nil {
+		t.Fatalf("closeServerWithErr(server) = %v, want <nil>", err)
+	}
+	if err := closeServerWithErr(server); err == nil {
+		// Duplicated closes should gracefully issue an error.
+		t.Fatalf("closeServerWithErr(server) = <nil>, want non-nil")
+	}
+}