In　the　paper,　we　propose　a　deterministic　approximation　algorithm　for　maximizing　a　generalized　monotone　submodular　function　subject　to　a　matroid　constraint.　The　function　is　generalized　through　a　curvature　parameter　c　is　an　element　of[0,　1],　and　essentially　reduces　to　a　submodular　function　when　c　=　1.　Our　algorithm　employs　the　deterministic　approximation　devised　by　Buchbinder　et　al.　[3]　for　the　c　=　1　case　of　the　problem　as　a　building　block,　and　eventually　attains　an　approximation　ratio　of　1+g(c)(x)+　Delta　center　dot　[3+c-(　2+c)x-(　1+c)g(c)(x)]　/　2+c+(1+c)(1-x)　for　the　curvature　parameter　c　is　an　element　of[0,　1]　and　for　a　calibrating　parameter　that　is　any　x　is　an　element　of[0,　1].　For　c　=　1,　the　ratio　attains　0.5008　by　setting　x　=　0.9,　coinciding　with　the　renowned　performance　guarantee　of　the　problem.　Moreover,　when　the　submodular　set　function　degenerates　to　a　linear　function,　our　generalized　algorithm　always　produces　optimum　solutions　and　thus　achieves　an　approximation　ratio　1.