China Railway Express (CR Express) is a pioneer of the Silk Road Economic Belt and the 21st Century Maritime Silk Road. The intermodal container terminal system consisting of a maritime terminal and a railway terminal is investigated in this paper. It connects the shipping route and the CR Express route. Typically, there are two container accumulation modes in the railway terminal to dispatch a train, i.e., the fixed-length and the fixed-time container accumulation modes. The intermodal container terminal system can be formulated as the two-echelon dual-channel supply chain model. The steady-state probability matrix is obtained by solving the equilibrium equations. The cooperation between the maritime terminal and the railway terminal is considered to accelerate the accumulation of the containers. The total revenue of the two terminals is used as the key system performance indicator. Numerical experiments are conducted to compare the fixed-length and the fixed-time container accommodation modes. The situations with and without cooperation between two terminals are also compared in the two container accumulation modes, respectively.