diff --git a/src/bin/pg_verifybackup/t/007_wal.pl b/src/bin/pg_verifybackup/t/007_wal.pl
index 12ca30139c5..10da5ca5041 100644
--- a/src/bin/pg_verifybackup/t/007_wal.pl
+++ b/src/bin/pg_verifybackup/t/007_wal.pl
@@ -105,4 +105,26 @@ $primary->command_ok(
 command_ok([ 'pg_verifybackup', $backup_path3 ],
 	'WAL verification succeeds with separate pg_wal.tar');
 
+# Same with client-side gzip compression.  pg_basebackup writes pg_wal.tar.gz
+# as several concatenated gzip members.
+SKIP:
+{
+	skip "gzip compression not supported by this build", 2
+	  if !check_pg_config("#define HAVE_LIBZ 1");
+
+	my $backup_path4 = $primary->backup_dir . '/test_tar_gz_wal';
+	$primary->command_ok(
+		[
+			'pg_basebackup',
+			'--pgdata' => $backup_path4,
+			'--no-sync',
+			'--format' => 'tar',
+			'--gzip',
+			'--checkpoint' => 'fast'
+		],
+		"tar backup with separate pg_wal.tar.gz");
+	command_ok([ 'pg_verifybackup', $backup_path4 ],
+		'WAL verification succeeds with separate pg_wal.tar.gz');
+}
+
 done_testing();
diff --git a/src/fe_utils/astreamer_gzip.c b/src/fe_utils/astreamer_gzip.c
index bc3d53076e1..5fdf0e27872 100644
--- a/src/fe_utils/astreamer_gzip.c
+++ b/src/fe_utils/astreamer_gzip.c
@@ -333,6 +333,14 @@ astreamer_gzip_decompressor_content(astreamer *streamer,
 							  mystreamer->base.bbs_buffer.maxlen, context);
 			mystreamer->bytes_written = 0;
 		}
+
+		/*
+		 * The input can be several gzip members one after another, which is
+		 * what pg_basebackup writes for pg_wal.tar.gz.  Get ready for the
+		 * next one.
+		 */
+		if (res == Z_STREAM_END && inflateReset(zs) != Z_OK)
+			pg_fatal("could not reset compression stream");
 	}
 }