The cryostat in the China Fusion Engineering Testing Reactor (CFETR) provides vacuum and low temperature operating conditions for the superconducting magnet system. A high pressure in the cryostat can increase the Rayleigh number (Ra) and cause the natural convection within the continuous hypothesis. A three-dimensional model, using incompressible ideal gas model and realizable k-ε model, is built to simulate the natural convection between the superconducting magnet system and the thermal shield within the temperature range of 4.5-80 K. The distributions of velocity field and heat flux on different surfaces of superconducting magnet system are obtained under different Rayleigh number conditions. The results show that the areas with large natural convection velocity mainly locate near the Central Solenoid (CS) coils and at the bottom of vacuum chamber. When the Rayleigh number ranges from 104 to 1010, the maximum velocity of helium gas decreases, while the heat flux on walls of superconducting magnets increases rapidly, and the heat flux on walls of PF-1, CS and TF coils is more affected by pressure, which needs to be considered in designing the safety system.