In　this　paper,　we　consider　the　effect　of　diffusion　on　the　permanence　and　extinction　of　a　non-autonomous　nonlinear　growth　rate　single-species　dispersal　model　with　time　delays.　Firstly,　the　sufficient　conditions　of　the　permanence　and　extinction　of　the　species　are　established,　which　shows　if　the　growth　rate　and　dispersal　coefficients　is　suitable,　the　species　is　permanent,　on　the　contrary,　it　is　extinction.　Secondly,　an　interesting　result　is　established,　that　is,　if　only　the　species　in　some　patches　even　in　one　patch　is　permanent,　then　it　is　also　permanent　in　other　patches.　Finally,　some　examples　together　with　their　numerical　simulations　show　the　feasibility　of　our　main　results.　(c)　2006　Elsevier　Ltd.　All　rights　reserved.