A transient, moving laser beam, three dimensional laser remelting mathematical model considering convection, diffusion and phase change process in laser melting pools and substrate was developed, which is suitable for the prediction of fluid flows, temperature field, liquid fraction field and phase change in solid, liquid and mash zone. Based on the mathematical mode, this paper developed an fix-grid numerical method. This method need not trace the interface between solid and liquid, and can consider the effect of latent heat released during phase change. The agreement of melting pool depth between prediction and experiment validates the model. The simulation shows that the surface tension and buoyancy drive the liquid metal fluid forming two set eddies in the transverse section, i.e. the first order recirculating,and the second order recirculating. The first order recirculating makes the pool wide and shallow and the second order recirculating digs a pit in the bottom of the pool. The experimental results show a good agreement with the model simulation.