Laser polishing is a new surface treatment technology which can effectively improve the surface roughness of metal materials. In order to investigate the effect of laser polishing on the surface morphology of 316L stainless steel. In this paper, a two-dimensional axisymmetric transient laser polishing numerical model is developed. Using a moving Gaussian pulsed laser as a heat source. Constructing model surfaces with high consistency with actual material surface contours. The temperature distribution, velocity and the evolution of molten pool on the surface of the polishing model were simulated. The results show that when the surface curvature of the melt pool is large, the capillary force dominates the flow of the molten material from the crest to the trough; when the surface of the melt pool is smooth, the thermocapillary force dominates the flow of the molten material to the edges of both sides of the melt pool. The depth and duration of the molten pool have a great influence on the polishing effect, the surface roughness results are worse when the molten pool depth is small and the duration is short and when the molten pool depth is large and the duration is long. A set of laser parameters with better polishing results were analyzed and experimented, and it is found that the surface roughness of the material is reduced by 69.5% after polishing, which verifies that the numerical simulation model has a high accuracy.