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CUDA is a new computing architecture introduced by NVIDIA Corporation, aiming at general purpose computation on GPU. The architecture has strong compute power in the compute-intensive applications and data-intensive applications, so in recent years, how the framework is applied to the scientific computing has become a hot research. The iterative method for solving systems of linear equations in engineering and scientific computing has a very far-ranging application. The algorithm provided with high computing intensity and parallelism is very suitable for CUDA architecture. In this paper, Jacobi iterative method is implemented on CUDA-enable GPU. The experimental results show that this iterative method can effectively make use of the CUDA-enable GPU computing power and achieve good performance.