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Game tree search is a classical problem in the field of game theory and artificial intelligence. Fast game tree algorithm is critical for computer games asking for real-time responses. In this paper, we focus on how to leverage massive parallelism capabilities of GPUs to accelerate the speed of game tree algorithms and propose a concise and general parallel game tree algorithm on GPUs. The performance model of the algorithm is presented and analyzed theoretically. We also implement the algorithm for a real computer game called Connect6 and use it to verify the effectiveness and efficiency of our algorithm. Experiments support our theoretical results and show good performance of our approach. Compared to classical CPU-based game tree algorithms, our algorithm can achieve speedup of 70.8 in case of no pruning. When pruning is considered (which means the practical performance of our algorithm), the speedup can reach about 7.0. The insight of our work is that using GPUs is a feasible way to improve the performance of game tree algorithms.