In the post-COVID-19 era, port congestion has become the norm, and the digitalization of shipping has accelerated due to the sporadic occurrence of global outbreaks. How to promote blockchain technology to improve the efficiency of port customs clearance and logistics transparency has become a hot research question. In this paper, we investigate the value of blockchain-based vertical cooperation led by a port or a shipping company in a one-to-two shipping service competition model. Meanwhile, we discuss consumer surplus and social welfare under different cooperation frameworks. We find that i) investment in blockchain technology can significantly increase the profits of port and shipping supply chain participants. ii) From the point of view of profit, when the investment efficiency of ports and shipping companies satisfies a certain relationship, there is a balanced strategy for both parties to invest in blockchain technology. iii) The more intense the competition for the services of shipping companies on the blockchain nodes, the lower the level of blockchain technology to improve the logistics capabilities of the port and shipping supply chain node companies. iv) From the perspective of maximizing consumer surplus and social welfare, the port’s investment in blockchain technology brings more consumer surplus and social welfare. The abovementioned findings can provide a reference for the daily operations of ports and shipping companies and present decision support for the government to formulate blockchain technology promotion policies.