The choice of emission control technology in a port supply chain under a cap-and-trade scheme considering low-carbon preferences of customers, is explored in this study. In port areas, the port supply chain consisting of one port and one ship can adopt either shore power (SP) or low sulfur fuel oil (LSFO) to reduce emissions. The economic and social performance of the port supply chain when either SP or LSFO is implemented is compared under three different game models (port-leader Stackelberg game, ship-leader Stackelberg game and the Nash game). The obtained results show that the profits and emissions in the Nash game are higher than those in the other two games. When environmental concern is relatively small, social welfare in the Nash game is the highest, while social welfare in the one-party-dominant structure is superior to that in the Nash structure, under high environmental concern. When the customers’ low-carbon preferences and carbon prices are low, both the supply chain’s profits and carbon emissions when LSFO is used are higher than those from using SP. From the perspective of social welfare maximization, in general, LSFO is preferred when carbon price, customers’ low-carbon preference and environmental concern are all low or are all high. Otherwise, SP is the optimal decision. The findings can provide insights for governments in formulating emission control policies according to their own interests.