The　periodic　solution　and　global　stability　for　a　nonautonomous　competitive　Lotka-Volterra　diffusion　system　is　considered　in　this　paper.　By　using　of　Brouwer　fixed　point　theorem　and　constructing　a　suitable　Liapunov　function,　under　some　appropriate　conditions,　the　system　has　a　unique　periodic　solution　which　is　globally　stable.　(C)　2010　Elsevier　Inc.　All　rights　reserved.