Given the in-depth advancement of the “Belt and Road” initiative, cooperation among countries along the initiative is increasing. The strategic maritime transport passage is closely related to the interests of relevant countries. The games between countries along important transport passages in terms of the pursuit of geopolitical rights and interests occur frequently. This paper establishes an evolutionary game model of the strategic maritime transport passages taking the Strait of Hormuz as an example and explores the game of the countries on both sides of the strait. By analysing their behaviour and possible strategies, the evolutionary stable strategy for each country is obtained. Recommendations are made to aid with the relevant rights and interests of related countries.