Abstract: Laser Additive Manufacturing (LAM) technology is very suitable for the near net forming of complex integral components and the rapid repair of high value-added damaged parts. However, the complex dynamic solidification process in the molten pool of LAM significantly affects the final microstructure of the formed parts, thereby restricting its service performance. A multi-scale mathematical model that integrates a macro heat and mass transfer and a multi-phase fields was established for the direct energy deposition by laser (DED-L) process of Inconel 718. The direct coupling of the macro-micro temperature field of the molten pool is solved. The two-dimensional global quantitative microstructure simulation of the molten pool is realized based on MPI parallel program design. The grain evolution process in the solidification of the molten pool is studied. The results show that the simulated molten pool size and solidification interface morphology are in good agreement with the experimental results. The morphology of solidification interface and the preferred orientation of crystal are important factors affecting the grain evolution. On the cross-section of the molten pool, the smaller the angle between the preferred orientation and the direction of temperature gradient, the more dominant the grain growth, because the solidification process is mainly driven by the direction of temperature gradient. On the longitudinal-section of the molten pool, the grain growth shows the characteristics of bending growth and "upper triangle". The gradual change of temperature gradient leads to the grain bending, and the competition behavior of adjacent grains determines the grain morphology. In this work, the mechanism of grain evolution in metal LAM is elucidated, which helps to clarify the thermophysical, chemical and metallurgical processes of additive manufacturing, and provides theoretical guidance for the prediction and control of microstructure. In addition, the multi-scale mathematical model can also be applied to the LAM process of other metal materials.