Almost　periodic　solution　of　a　three-species　competition　system　with　grazing　rates　and　diffusions　were　investigated　by　using　the　method　of　upper　and　lower　solutions,　the　Schauder　fixed　point　theorem　as　well　as　Lyapunov　stability　theory.　Sufficient　conditions　guaranteeing　the　existence　and　stability　of　the　strictly　positive　space　homogenous　almost　periodic　solution　of　the　system　were　obtained,　and　some　known　results　were　improved.