Inspired by the idea of game learning, this paper studies the Cournot game model of the multi-oligopoly market and studies the realization of the Nash equilibrium by using adaptive differential evolution algorithm based on relaxation strategies. The realization path of Nash equilibrium is attained through an adaptive differential evolution based on a relaxation strategy procedure applied to an objective function with best response dynamics. Among them, the objective function is derived from the sum of the payoff changes of each oligopoly under best response decisions. And theoretically proved that the Nash equilibrium is the optimal solution of the objective function.