In order to solve the problems that nonlinear static output feedback H∞control design process is complex,and its difficult to obtain the globally optimal solution and so on,a new approach is presented to design the controller.An approach of Sum of Squares (SOS) is used to analyze the H∞performance of polynomial nonlinear system.Taking the system L2 performance as the objective function,Genetic Algorithm (GA) is used to optimize the control parameters.Simulation results show that the designed controller achieves the optimal L2 performance of the polynomial nonlinear system.