This paper addressed the vessel schedule recovery problem (VSRP) for container liners suffering delays caused by disruptive incidents, and introduced the shipping carbon trading mechanism. A dual-objective optimization model for VSRP was established to minimize voyage schedule recovery costs and maximize customer service level. For scenarios with anticipated operational disruptions, the optimal combined strategy consisting of speed adjustment, port skipping and port swapping was solved. An improved adaptive non-dominated sorting genetic algorithm II (NSGA-II) was designed to solve the proposed model. Multiple scenario-based numerical examples verify the effectiveness of the proposed model and improved algorithm in this paper. Numerical results show that different durations of anticipated disruptions correspond to distinct optimal combined strategies for schedule recovery. Under the dual-objective optimization without preference, utilizing information on anticipated disruptions can reduce voyage recovery costs by 18.31% on average. Sensitivity analysis shows that when the carbon trading price rises, both the schedule recovery cost and vessel carbon emissions decrease simultaneously if the preference weight of the carbon emission reduction objective is large. Besides, an increase in carbon quotas will directly cut down the schedule recovery cost. In contrast, when the preference weight of the carbon reduction objective is small, carbon emissions follow a trend of decreasing first and then increasing. The research conclusions can provide theoretical support and decision-making references for shipping enterprises to formulate schedule recovery schemes under operational disruptions.