The Belt and Road (B&R) initiative provides a great opportunity for facilitating the development of the maritime industry. Ports, as the main components of the global maritime logistics system, have attracted attention from both industry and academia in relation to the evaluation of their role in maritime shipping networks. To assess the importance of ports along the Maritime Silk Road (MSR), this paper constructs a container shipping network based on the service information of 16 world-leading container liners and analyzes the disparity of ports based on the topological features of the network. A novel multi-centrality-based indicator is proposed to analyze the centrality of ports along the MSR from a more comprehensive perspective, and the obtained results are further verified by using vulnerability analysis. The results indicate that the Port of Hong Kong, Port of Singapore, Port of Shenzhen, and Port Klang are at the center of the MSR container shipping network. The vulnerable ports identified by different methods are largely consistent. This study provides a reference for the management of ports along the MSR and a theoretical basis for future optimization of container shipping networks in other areas of the world.