A numerical simulation study on the field of Nd 3+ concentration in the melt and the crystal by using FDM (finite differential method) during the growth of Nd∶YAG crystal by Cz (Czochralski) method was reported. At first, the mathematical model of the growth of Nd∶YAG crystal was given, then the equations with no dimensions were given. Finally, the boundary condition was given and the equations were solved by FDM. The simulation program was given by above method, and then the change of the field of the Nd 3+ concentration in the melt and the crystal was described by simulation program. The effect of processing conditions on the above field in the melt was analyzed.