Intercontinental liner container shipping service connects trades between different continents in the global logistic system. This paper proposes a single intercontinental service design problem that aims to jointly determine the optimal serviced ports from a set of candidate ports, the port rotation, the ship sailing speed on each voyage between adjacent serviced ports and the number of containers transported for each type of shipping demand. A mixed integer linear programming model is formulated for the proposed problem based on mild assumptions to maximize the service profit, which is calculated as the freight revenue minus the total operating cost that includes port stay cost, container handling cost, bunker consumption cost, and other ship operating costs. The formulated model is also able to produce a service route with a more general topological structure than the simple cycle or butterfly cycle routes considered in most current studies. In view of the unique features of the model, a tailored and exact branch-and-cut algorithm is developed based on Benders decomposition to expedite the model solution. Numerical experiments demonstrate the efficiency of the developed branch-and-cut algorithm and show the applicability of the proposed model for designing the intercontinental liner shipping services. The e-companion is available at https://doi.org/10.1287/trsc.2018.0831 .