Against the backdrop of the global trend towards green and low-carbon transformation, the international shipping industry is facing increasingly stringent environmental regulations. This study employs the Stackelberg game model to investigate the impact of the European Union's maritime carbon tax policy on the behavior of China Ocean Shipping Company (COSCO). In the model setup, the European Union is considered the market leader, determining the optimal carbon tax rate in advance, while COSCO, as a market follower, adjusts its transportation volume and operational strategies in response to the cost changes induced by the carbon tax. The study constructs a decision-making game framework under the influence of the carbon tax by establishing market demand functions, cost functions, and the EU's objective function. Utilizing MATLAB for numerical simulation analysis, the research proposes differentiated phased response strategies for the short, medium, and long terms. The aim is to provide a reference for the transformation and upgrading of Chinese shipping enterprises in the context of green regulations through a combination of institutional analysis and model calculation. Chinese shipping enterprises need to balance emission reduction targets with economic benefits through legal compliance, low-carbon technology innovation, and international cooperation, in order to cope with the global trend towards low-carbon shipping.