Logic　key　hierarchy　is　a　leading　scheme　for　key　distribution　in　secure　multicast.　In　this　paper,　an　improved　Logic　key　hierarchy　scheme,　based　on　one-way　hash　function,　is　proposed.　Besides　its　simplicity,　the　improved　scheme　can　reduce　key　server＇s　average　cost　by　about　1/3.　Moreover,　a　batch　update　algorithm　for　this　improved　scheme　is　also　presented,　and　its　performance　is　evaluated　through　experiments.　Compared　with　batch　update　algorithm　in　Logic　key　hierarchy　scheme,　it　shows　the　algorithm　presented　in　this　paper　can　reduce　key　server　cost　by　at　least　1/3.