This paper presents a method for evaluating the nash equilibrium of the Cournot model for N-Gencos in wholesale electricity market. In wholesale electricity market, the strategies of N-Gencos can be applied to the game model under the conditions, which the Gencos determine their strategies to maximize their benefit. Generally, the Lemke algorithm has known as the approach to evaluate the mixed nash equilibrium in the only two-player game model. In this paper, we have developed the necessary condition for obtaining the mixed nash equilibrium of N-player by using the Lemke algorithms. However, it is difficult to find the mixed nash equilibrium of two more players by using the analytic method since those have the nonlinear characteristics. To overcome the above problem, we have formulated the object function satisfied with the proposed necessary conditions for N-player nash equilibrium and applied the modified particle swarm optimization (PSO) method to obtain the equilibrium for N-player. To present the effectiveness the proposed necessary condition and the evaluation approach, this paper has shown the results of equilibrium of sample system and the cournot game model for 3-players.