Port-centric intermodal transshipment hubs are significant nodes in the global freight network and are likewise the gateway to a country’s external communications. It is vital to increase the service capacity of PCITHs, and it is necessary to assess the service capacity of port-centric intermodal transshipment hubs to respond to the growth of economies and global freight needs. This study provides a detailed definition of port-centric intermodal transshipment hubs through a review of relevant kinds of works from the literature and analyzes their primary functions. Based on the research perspective of sea–rail intermodal transportation, the three evaluation dimensions of service capacity of port-centric intermodal transshipment hubs are divided into radiation scale capacity, transportation connection capacity, and resource integration capacity, focusing on the functions of cargo aggregation, cargo transfer, and connection of different transportation modes. The service capacity evaluation indicators were then selected based on the three dimensions. The subjective and objective weightings were calculated by the G1 weighting method and the modified CRITIC method, and the combination weightings were determined based on game theory. The service capability of port-centric intermodal transshipment hubs was evaluated by the fuzzy matter element method, and the evaluation results were quantified by the Euclidean closeness degree. Finally, through the barrier degree model, the current indicators of PCITHs that urgently need improvement were explored, and targeted improvement suggestions are proposed in this paper. The results show that Tianjin Port has the highest service capacity, followed by Ningbo Zhoushan Port. The port rail dedicated line mileage is the most critical area that needs attention in Ningbo Zhoushan Port and Qingdao Port. Tianjin Port needs to improve the container sea–rail transportation volume, while Guangzhou Port and Xiamen Port need to improve the sea–rail container handling capacity.