<p>Carbon tax is a potential and effective market-based measure for reducing carbon emissions, but it may also impose economic burdens on shipowners. In this study, speed optimization was carried out under the carbon tax scheme, one of the most direct and effective measures to reduce emissions and variable costs. This study proposes two carbon pricing schemes (fixed and progressive); the main innovation lies in improving the design of the progressive carbon tax to make it more strictly in line with the polluter pays principle and the ability-to-pay principle. On the premise of ensuring the efficiency of ship transportation, this paper improves the genetic algorithm to make it more suitable for speed optimization and optimizes the speed of sample ships of different sizes. The main research results show that: (1) Both carbon tax schemes significantly increase the ship’s variable costs. (2) If the speed of certain segments is reduced after optimization, the speed of other segments must be increased to ensure annual transportation efficiency and maintain the competitiveness of ship operators. (3) After optimization, at least 10.12% of emission reduction and 8.80% of variable cost savings were achieved. The impact of progressive carbon taxes on the percentage of emission reduction and the percentage variable cost savings will intensify as the ship size increases. (4) The progressive carbon tax alleviates the economic disparities between high- and low-emission ships. This research provides quantitative evidence supporting the carbon tax in the shipping industry formulation, particularly emphasizing how the progressive carbon tax can balance environmental objectives with industry competitiveness. Large ships’ emissions are the top priority for emission reduction in the shipping industry, the progressive carbon tax can more effectively reduce emissions from large ships, and it may be more applicable to the shipping industry than the fixed carbon tax.</p> Graphical abstract <p></p>