To sustain the development of maritime transportation, “green ports,” which operate with a good balance between environmental impact and economic interests, have been the focus of port operators and government agencies and are required to look into energy saving and emission reduction initiatives. One such reduction strategy proposed by the International Maritime Organization suggested imposing a carbon emission tax on ports as a long-term solution to reduce carbon emissions, but this would definitely increase the operating cost of ports. Quay cranes (QCs), as one type of handling equipment, play an important role in the service efficiency and carbon emission of ports. Therefore, this paper makes an effort to explore the study of the integrated berth allocation and QC assignment problem with the consideration of carbon emission taxation. This problem is formulated as a biobjective integer programming model, aimed at minimizing the total completion delay of all tasks and the total operating costs for all QCs. Finally, numerical experiments are performed to assess the applicability of the proposed models and evaluate the efficiency of the developed solution algorithm.