Abstract: Due to its good creep strength, Mo single crystal is used for component of the fuel element of the space-thermionic reactor. The single crystal connection of the material and the reduction of stray grain formation in the weld joint is the main way to improve the service life of the fuel element. In this paper, based on the theory of probabilistic nucleation and dendrite growth, the cellular automata (CA) method was used to simulate the rapid solidification process of Mo welding. The simulation results show that CA method is an effective and reliable research method that can simulate the Mo welding process and visualize the weld growth process, which is helpful for the optimization of weld microstructure and the improvement of the mechanical properties of the materials.