diff --git a/ChangeLog.md b/ChangeLog.md
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -1,6 +1,11 @@
 # Revision history for http2-tls
 
 
+## 0.5.8
+
+* Send close_notify after an HTTP/2 connection the server ends.
+  [#28](https://github.com/kazu-yamamoto/http2-tls/pull/28)
+
 ## 0.5.7
 
 * A server can be stopped through `settingsInstallShutdownHandler`: the
diff --git a/Network/HTTP2/TLS/Server.hs b/Network/HTTP2/TLS/Server.hs
--- a/Network/HTTP2/TLS/Server.hs
+++ b/Network/HTTP2/TLS/Server.hs
@@ -58,6 +58,7 @@
 import Control.Concurrent.STM (STM, atomically, check, newTVarIO, readTVar, retry, writeTVar)
 import qualified Control.Exception as E
 import Data.ByteString (ByteString)
+import Network.HTTP2.Client (HTTP2Error (..))
 import Network.HTTP2.Server (
     Server,
     connectionWindowSize,
@@ -193,7 +194,7 @@
     E.bracket
         (allocConfigForServer settings0 mgr send sendWith recv recvWith mySockAddr peerSockAddr)
         freeConfigForServer
-        (\conf -> H2Server.runWith goAway sconf conf server)
+        (\conf -> endedNormally $ H2Server.runWith goAway sconf conf server)
   where
     sconf =
         defaultServerConfig
@@ -231,7 +232,7 @@
     E.bracket
         (allocConfigForServer settings0 mgr send sendWith recv recvWith mySockAddr peerSockAddr)
         freeConfigForServer
-        (\conf -> H2I.runIOWith goAway sconf conf action)
+        (\conf -> endedNormally $ H2I.runIOWith goAway sconf conf action)
   where
     sconf =
         defaultServerConfig
@@ -283,6 +284,14 @@
                 stop >> atomically (writeTVar var True)
     return
         (settings{settingsInstallShutdownHandler = install}, readTVar var >>= check)
+
+-- | http2 ends a connection which has run its course with
+--   'ConnectionIsClosed'.  Taken as returning, so that close_notify is
+--   sent after it, as for any other action.
+endedNormally :: IO () -> IO ()
+endedNormally = E.handle $ \e -> case e of
+    ConnectionIsClosed -> return ()
+    _ -> E.throwIO e
 
 ----------------------------------------------------------------
 
diff --git a/http2-tls.cabal b/http2-tls.cabal
--- a/http2-tls.cabal
+++ b/http2-tls.cabal
@@ -1,6 +1,6 @@
 cabal-version: >=1.10
 name:          http2-tls
-version:       0.5.7
+version:       0.5.8
 license:       BSD3
 license-file:  LICENSE
 maintainer:    Kazu Yamamoto <kazu@iij.ad.jp>