Liu, Zh.C. Qiang, J. JACoW Geneva, Switzerland 978-3-95450-182-3 10.18429/JACoW-IPAC2017-THPAB027 English 3756-3759 THPAB027 Contribution to a conference proceedings 2017 2017-05 http://dx.doi.org/10.18429/JACoW-IPAC2017-THPAB027 http://jacow.org/ipac2017/papers/thpab027.pdf The symplectic tracking model can preserve phase space structure and reduce non-physical effects in long term simulation. Though this model is computationally expensive, it is very suitable for parallelization and can be accelerated significantly by using Graphic Processing Units (GPUs). Using a single GPU, the code achieves a speedup of more than 400 compared with the time on a single CPU core. It also shows good scalability on a GPU cluster at Oak Ridge Leadership Computing Facility. In this paper, we report on the GPU code implement, the performance test on both single-GPU and multi-GPU cluster, and an application of beam dynamics simulation.