In　the　present　paper,　several　sufficient　conditions　are　obtained　for　the　existence　and　exponential　attractivity　of　a　unique　κ-almost　periodic　sequence　solution　of　discrete　time　neural　network.　Our　results　generalize　the　corresponding　results　about　almost　periodic　sequence　solution　in　common　sense.　It　is　shown　that　discretization　step　κ　affects　the　dynamical　characteristics　of　discrete-time　analogues　of　continuous　time　neural　networks　and　exponential　convergence　is　dependent　on　small　discretization　step　size.　Our　results　on　exponential　attractivity　of　κ-almost　periodic　sequence　solution　can　provide　us　with　relevant　estimates　on　how　precise　such　networks　can　perform　during　real-time　computations.　Finally,　computer　simulations　are　performed　in　the　end　to　show　the　feasibility　of　our　results.　©　2006　Springer　Science+Business　Media,　Inc.