Over the past few decades, the number of liquefied natural gas (LNG) ships and terminals has been increasing, playing an important role in global clean energy transportation. However, the traffic capacity of LNG shipping in port areas is limited because of its high safety requirements. In view of this problem, a novel model is proposed to study the ship traffic in a port area by combining cellular automaton (CA) and multi-agent methods. Taking the CNOOC Tianjin LNG Terminal as an example, the ship traffic in Tianjin Port is simulated. Based on the simulation results, the LNG ship traffic capacity and its impact on the general shipping traffic flow under different special traffic rules are obtained. This model can provide theoretical support for optimising the port traffic organisation for LNG ships.