Solving linear equations is a common problem in the fields of science and engineering. Accelerating its solving process is of great significance. Modern GPUs are high performance many-core processors fit for large scale parallel computing. They provide us a novel way for accelerating the solving process. A GPU based parallel Jacobi’s iterative solver for dense linear equations is presented in this paper. First, we introduce the backgrounds for accelerating solving linear equations together with GPUs and the corresponding parallel platform CUDA on it. Then we implement Jacobi’s iterative method on CUDA. Finally, we compare the experimental results of CUDA programs on GPU with traditional programs on CPU. Experiments show that it obtains a speedup of approximately 59 times with single floating point at a low precision, 19 times with double at a high precision.