In　this　paper,　we　consider　a　discrete　Gilpin-Ayala　type　population　model.　Assume　that　the　coefficients　in　the　system　are　almost　periodic　sequences,　we　obtain　that　r　of　the　species　in　the　system　are　permanent　and　stabilize　at　a　unique　strictly　positive　almost　periodic　solution　of　the　corresponding　subsystem,　which　is　globally　attractive,　while　the　remaining　species　are　driven　to　extinction.　©　2013　Copyright　Taylor　and　Francis　Group,　LLC.