We have developed a two-dimensional numerical model to simulate the evolution of grain structure observed during the laser additive manufacturing process. A cellular automata method is used to describe grain growth. The Goldak heat source model is adopted to calculate the heat input during laser melting. A selective laser melting process which involves sequential deposition of powder layers on a polycrystalline substrate followed by their melting is examined. The influence of the heat source parameters on the evolution of grain structure is discussed. The simulation results are shown to be consistent with the experimental data describing the main characteristics of the grain structure. Keywords: Laser additive manufacturing, Grain growth, Solidification, Cellular automata, Evolution of grain structure