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Centrality has always been used in transportation networks to estimate the status and importance of a node in the networks, especially in the shipping networks. However, most of the studies only take the shipping network as an unweighted network or only considering the tie weights in the weighted networks, ignoring the truth that both the number of ties and tie weights contribute to the centrality in weighted shipping networks. Therefore, we proposed a new method combining both the number of ties and tie weights to assess the node centrality based on effective distance by integrating the studies of Opsahl et al., (2010) and Du et al., (2015). An empirical analysis of shipping network at the country level for the 21st-centrtury Maritime Silk Road (MSR) was performed. The result of correlation analysis between country's degree centrality and the Liner Shipping Connectivity Index (LSCI) published by the United Nations Conference on Trade and Development (UNCTAD) proved the superiority of our method compared to the traditional centrality metrics. In weighted networks, both the number of ties the tie weights should be considered by adjusting the parameters. The method proposed in this study can also be used to nodes' status and importance estimation of various networks in other fields.