By using the Matlab and Simulink software, this work numerically simulates the dynamic situation of Sapphire crystal growth. The results of the simulation are then compared to the real diameter of grown record and refer to fine-tune the parameters of crystal growth, internationally. The parameters of sapphire crystal growth include the slew rate, the PID of automatic diameter controller, the OID of power controller, smoothing filter, etc. As the slew rate increases, the diameters of the growing crystal become stable. The diameter variation, with respect to the crystal length, even turns into better after the fine-turn of the PID and the smoothing filter parameters.