Under the background of carbon peak carbon neutrality, the competition among ports is not only the competition among terminal scale, throughput, and service level, but also the competition of low energy consumption and low pollution, and with the development of China’s carbon trading mechanism, the cost of carbon emission has become more and more a part of the enterprise that cannot be ignored. In this paper, the berths and shore bridges of the port are taken as the target variables, and the fuel consumption in the process of ships traveling to the port is inferred according to the assumed conditions, and the BAP model under the carbon peak carbon neutrality is deduced, and the relevant constraints are proposed. The initial population is randomly generated, and the first generation of offspring population is obtained through the selection, crossover and mutation operations of multi-objective genetic algorithm, which then continues until the end conditions of the program are satisfied. Through the empirical method, comparing the effect of carbon cost optimization scheme generated by multi-objective genetic algorithm and traditional method, the value of the objective function under the multi-objective genetic algorithm model decreased by 10.48%, the operation cost of the port decreased by 4.54%, the cost of the ship’s in-port time decreased by 24.9%, and the ship’s average in-port time decreased by 11.01%, as compared with the traditional allocation scheme. The multi-objective genetic optimization model of berth shore bridge considering carbon cost can shorten the ship’s time in port, which reduces the carbon emission from the side and achieves the promotion purpose of green port. In the model sensitivity analysis, with the increase of carbon trading price, the four indicators F, F1, F2 and T also showed linear growth, with the growth rate of 17.24%, 18.44%, 14.37% and 18.02%, respectively, and the model sensitivity is good.