This　paper　presents　GM　(1,　N)　models　with　linear　cross　effect　and　nonlinear　cross　effect,　and　discusses　the　difference　of　driving　factors　between　these　two　types　of　models　to　solve　the　cross　effects　of　GM　(1,　N)　model.　The　model　with　a　linear　cross　effect　in　this　paper　preserves　the　solution　of　whitenization　in　the　GM　(1,　1)　model.　While　the　model　with　nonlinear　cross　effect　integrates　the　sequences　of　systemic　features,　driving　factors,　and　the　cross　effect　of　these　driving　factors.　While　applying　support　vector　machine　(SVM)　regression,　it　transfers　the　nonlinear　relationship　among　these　sequences　to　a　linear　relationship.　To　test　the　GM　(1,　N)　model　that　is　based　on　support　vector　machine　(SVM)　with　nonlinear　effect,　the　study　applies　it　to　forecast　the　total　output　of　the　pharmaceutical　industry.　The　range　of　the　data　is　selected　from　2005-2017,　which　the　data　from　2005-2013　are　used　to　fit　into　the　model.　The　GM　(1,　N)　model　based　on　SVM　with　nonlinear　cross　effect　achieves　0.6566　and　0.2956　in　its　fitted　total　of　relative　error　and　the　forecast　total　of　relative　error,　respectively.　The　new　model　presents　a　more　accurate　analysis　on　fitting　and　forecast　precision　than　the　classic　GM　(1,　N)　model　and　GM　(1,　N)　with　the　linear　cross　effect　model.