A containment vessel is usually designed to prevent the potential leakage of radioactive gas in molten salt reactor. Understanding the gas flow characteristics in the containment vessel is beneficial for mastering the radioactive level and the early monitoring and diagnosing when radioactive leakage accident occurs. In this paper, the simplified physical model of the containment vessel in a molten salt reactor was set up, and the gas flow characteristics driven by natural circulation in the containment vessel was studied by CFD code. The results shown that, when the gas enters into the upper chamber from the lower chamber due to buoyancy force, the gas velocity will reach a maximum value of 1.7 m/s where local jet occurs. The mass flow rate of gas between the upper and lower chambers is about 24.0 kg/h and the average circulation time in the containment vessel is about 7.3 hours. It is interesting to note that, the gas tends to flow upward in those annulus gaps with larger hydraulic diameter or near to the central region, indicating that when leakage is near to those regions, it will be easier and faster to flow into the upper chamber. The results provide the reference and guidance for radioactive gas monitoring.