Modern computer technology empowers people to simulate additive manufacturing (AM) process at high fidelity, which has turned out to be a valid way to evaluate, anticipate, and design the AM processes. In this paper, we propose a new method to simulate the melting process of metal powder based AM. The physics is described using partial differential equations for heat transfer and Laminar flow. The level set methods are applied to track the motion of free surfaces between liquid and solid phases. The issues, including free surface evolution, phase transitions, and velocity field calculation are explored. The convergence problem is examined to improve the efficiency in solving this multiphysics problem.