[Objectives] Poiseuille flow is widely existed in industry, such as low Reynolds number pipeline flow, and pipeline transport is the key stage in deep-sea mining. The study of Poiseuille flow has guiding significance for the study of pipeline transport which is more comlex. [Methods] Moving Particle Semi-Implicit Method (MPS) is a meshless Lagrangian method, which uses Lagrangian particles to carry flow field information, so it can avoid the influence of mesh deformation on the calculation results. MPS has been widely applied in flows with free surface, multiphase flows and other flows. The meshless solver MLParticle-SJTU, which is developed independently based on MPS method, is used to simulate the Poiseuille flow in two-dimensional pipes under different Reynolds Numbers, by establishing inflow boundary and no-slip wall boundary, and the fluid is an incompressible Newtonian fluid. [Results] The simulation results show that after full development, the flow velocity profile is parabolic, and the error of the numerical simulation results is within 5% compared with the theoretical results under different Reynolds Numbers. [Conclusion] This indicates that it is effective and reliable that use the MPS method to simulate two-dimensional Poiseuille flows under the boundary conditions proposed in this paper.