In this paper, we consider the problem of finding good next moves in two-player games. Traditional search algorithms, such as minimax and α-β pruning, suffer great temporal and spatial expansion when exploring deeply into search trees to find better next moves. The evolution of genetic algorithms with the ability to find global or near global optima in limited time seems promising, but they are inept at finding compound optima, such as the minimax in a game-search tree. We thus propose a new genetic algorithm-based approach that can find a good next move by reserving the board evaluation values of new offspring in a partial game-search tree. Experiments show that solution accuracy and search speed are greatly improved by our algorithm.