Abstract: The performance of particle swarm optimization (PSO) algorithm is generally affected by its control parameters and velocity updating strategies. To further enhance the optimization performance of PSO, a self-adaptive PSO based on mixed knowledge (SPSO-MK) is proposed in this paper. In SPSO-MK, two different speed updating strategies are employed to balance the exploitation and exploration capabilities, in which one strategy is suitable for global search and the other is good at local search. The value of the inertia weight is updated by online knowledge coming from population information. The values of two acceleration factors are produced by prior knowledge so that the proposed SPSO-MK has better global and local search capability, respectively, in the early and late evolution phase. The experiments via 32 test functions are made, in which 10 PSO variants and 3 non-PSO algorithms are selected. It is shown from the experimental results that the proposed algorithm can attain the best performance among all compared algorithms. The proposed algorithm is also used to solve three Nash equilibrium problems of non-cooperative game, whose results illustrate that the proposed algorithm performs better than two DE variants. Moreover, the performance of SPSO-MK is significantly better than that of co-variance matrix adaptation evolutionary strategies (CMA-ES) on two Nash equilibrium problems and is significantly worse than that of CMA-ES on the third Nash equilibrium problem. The comparison with self-adaptive PSO shows that multiple velocity strategies (SAPSO-MVS) cannot perform better than the proposed algorithm on some problems. Therefore, SPSO-MK can effectively solve Nash equilibrium problems of non-cooperative game.