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Desmond is a high-performance program for molecular dynamics simulations (MDS). It provides an unprecedented combination of parallel scalability, simulation speed, and scientific accuracy. However, it still has much improvement space based on the fact that the computation of near non-bonded force (NNF) consumes most of the simulation time. NNF computation is the bottleneck of Desmond. In this paper, we address this problem with graphics processing units (GPU). To the authors' knowledge, this is the first try of accelerating Desmond with GPU. We propose two task decomposition approaches on different levels to accelerate the NNF computation on GPU, one pair-based and another more efficient particle-based. We employ several techniques to optimize the GPU NNF algorithm. Among these techniques, NNF updating conflicts reduction improves the performance best. Combining all the approaches and techniques, we obtain a final speedup of more than 10 on NNF computation and more than 3 on the whole Desmond.