Based on the lattice Boltzmann Method (LBM), a new moving boundary treatment is proposed by studying the influence of the moving boundary in a low-speed incompressible fluid. Simulating flow past a static cylinder, flow past a moving cylinder, and flow in a curved moving pipe shows that the LBM has high reliability and stability with moving boundary conditions. In order to reduce parallel computing time and take full advantage of the characteristics of the model, the solid grids are allocated according to the number of computing cores. Two parallel speedup ratios were tested, keeping the overall task volume unchanged to increase the number of cores and keeping the single-core task volume unchanged. In the first speedup ratio, the efficiency of the flow field calculation at 112 cores reached more than 80%. The second speedup ratio indicated that the proportion of communication in the program was tiny and suitable for large-scale parallel computing. The study of the moving boundary problem can effectively help solve the fluid-structure coupling problem. Due to the particularity of the model, it can be used to simulate the fluid-structure coupling problem of blood vessel flow effectively.