Abstract: The acceleration of the two-dimensional Laplace equation on the GPU platform was realized by using the finite element method based on Matlab platform. Through the analysis of the physical problem and the construction of the physical model, the generation of the stiffness matrix of the whole CSR format was completed. Parallel programming of the finite element problem was implemented on the Matlab platform using the mixed programming of Matlab and CUDA. Combining with the CuBlas numerical calculation library, the PCG algorithm was used to solve the large linear sparse system of the assembly, and the velocity potential of each lattice can be iterated efficiently. This algorithm not only gives full play to the efficiency of Matlab in numerical calculation, but also gives full play to the advantages of GPU in fine-grained parallel acceleration.