The Thorium-Based Molten Salt Reactor (TMSR) has been highlighted for its safety, economy, and nuclear nonproliferation. A program for developing the TMSR system has been launched in Shanghai Institute of Applied Physics, Chinese Academy of Sciences. In the TMSR system, mixtures of LiF and BeF2, termed FLiBe, are proposed and used as the primary coolant salt, in which tritium is produced mainly by the neutron reactions of lithium. In the TMSR system, at high temperatures, tritium can permeate through metal walls to the surroundings, leading to a potential radiological hazard. Thus, tritium control becomes a major problem hindering the development of the TMSR system. Evaluation of the tritium distribution is necessary for tritium control in the TMSR system. In this study, the Tritium Transport Analysis Code (TTAC) has been developed for simulating the tritium behaviors in the TMSR system (hence, the code TMSR-TTAC), such as tritium chemical forms in coolant salts, tritium transport behaviors, and tritium distribution in the system. The model code is developed by the MATLAB/SIMULINK package, and it is based on the mass balance equations of the tritium-containing species and hydrogen. TMSR-TTAC is benchmarked with the molten salt reactor model, which is based on Molten Salt Reactor Experiment designs. The results show that TMSR-TTAC has the ability to calculate the tritium distribution in the TMSR system.