The numerical simulation research on temperature field of crystal and melt by using finite differential method during the growth of Nd:GGG crystal by Cz (Czochralski) method was reported. At first, the mathematical model of the growth of Nd:GGG crystal was given, then the equations without dimensions were given. Finally, the boundary condition was given and the equations were solved by finite differential method. The simulation program was given by above method.Then the change of temperature field of crystal and melt was described by simulation program. The influence of technical conditions of temperature field in the crystal and melt was analyzed.