Dynamic simulation of Tokamak superconducting magnet system has been conducted to investigate the cool-down process from 300 to 80 K. The simulation focuses on the cool-down speed variations with respect to the global temperature gradients in the different coils; Toroidal Field (TF) coil, TF STructure (TF-ST), Central Solenoid (CS) and Poloidal Field (PF)/Correction Coil (CC) systems. As imposing the maximum temperature gradients dT max ≤ 50K, the speed should be adjusted, ensuring the limited mechanical stresses due to thermal contractions. So far, the process simulation of Tokamak cryogenic system has been concentrated on the Deuterium Tritium (DT) operation phase; therefore, it is necessary to revise the model to extend its capability for the cool-down; for example, the thermo-hydraulic properties of Cable-in-Conduit Conductor (CICC) for each coil, mechanical properties of materials for the magnet system. The cool-down process is implemented at the helium refrigerator by utilizing LN2 heat exchanger up to 80 K. Its speed is set at -0.8 K/hr as a baseline, which can be controlled by the global temperature gradients in the magnet system. The process will be on hold as dT max ≥ 50K, and resumed once dT max < 50K. The paper discusses the cool-down processes of the Tokamak and identifies the impact on the speed, dT i/dt, of each component.