With the advancement of global warming, the Arctic sea routes (ASRs) may open for the entire year. The ASRs will be far more competitive than they are now, and they will be the major international sea routes in the future. To date, most studies have researched the economic feasibility in the short term from a company’s perspective. To help to plan the shipping market in the future, we developed a three-stage model to simulate the trade demand of the ASRs for the long term. This model firstly considers the seasonal sea ice dynamics in the future and plans new paths for vessels shipping through the Arctic. Additionally, an improved trade prediction model was developed to adapt to the long-term forecasts. After verification, the accuracy of the model was found to be very high (R2 = 0.937). In comparison with another transportation cost model and a trade prediction model, our model was more reasonable. This study simulated the trade volumes of China, Europe (EU), and North America (NA) in 2100 with the ASRs open. The results show that the percentage of port trade can be up to 26% in representative concentration pathway (RCP)2.6, and the percentage of port trade can be up to 52% in RCP8.5.