We　investigate　the　problem　of　maximizing　a　gamma-submodular　function　subject　to　one　or　multiple　matroid　constraints　and　one　knapsack　constraint.　By　the　greedy　local　search　technique,　we　present　approximation　algorithms　with　constant　approximation　ratios.　When　gamma　=　1,　our　model　reduces　to　the　regular　submodular　maximization　problem　investigated　in　the　literature　under　the　same　type　of　constraints.　Our　results　therefore　contribute　towards　the　line　of　research　on　constrained　non-submodular　function　maximization.