In　the　present　paper,　we　investigate　the　relationship　between　the　globally　quasi-uniformly　asymptotic　stability　and　the　existence　of　almost　periodic　solutions　for　difference　systems.　Based　on　the　properties　of　almost　periodic　sequences,　several　criteria　are　established　for　the　existence　of　almost　periodic　solutions　for　difference　systems.　Then,　some　applications　in　population　dynamic　systems　are　presented　to　illustrate　our　main　results.　Finally,　we　end　this　paper　with　some　illustrative　examples　and　their　numeric　simulations.　Our　results　are　essentially　new　and　give　a　method　to　study　the　existence　of　almost　periodic　solutions　of　difference　equations.　The　method　used　in　the　present　paper　is　much　different　from　that　in　the　literature,　and　it　is　the　first　time　that　the　discrete　time　Lotka-Volterra　systems　have　been　studied　by　using　this　method.