The convex optimization,which serves as a new optimized method,can be fully applied to the game theory system,aiming at maximizing the payoff of the game systems (for all players).The two-person non-zero-sum matrix was introduced to describe the equivalent of payoff in the hypothetical game theory system for making quantitative analyses and getting maximal payoff of the system.A saddle point equation was created to be the critical equation of the optimal value of the game theory system and Newton's algorithm was used to simulate the game model.The simulation results show that,the results are consistent with the theoretical hypothesis values.The method was tested and verified to be feasible and accurate.The work is helpful for deeply understanding the game theory system and reasonably applying the convex optimization.