Medicine occupies an important position in people's lives, and its safety and effectiveness are directly related to people's lives and health. In recent years, with the frequent occurrence of unqualified vaccines, quality control in drug transportation has been paid more and more attention. Therefore, this paper constructs a tripartite evolutionary game model composed of government, pharmaceutical enterprises, and logistics enterprises and models behavioral strategies. The interaction between the two and the influence of different parameters on the evolution are simulated and analyzed. The results show that implementing a government punishment mechanism, inter-firm revenue sharing and drug failure rate will have different impacts on the outcome of the evolutionary stability strategy of pharmaceutical enterprises and logistics enterprises. These conclusions not only enrich the theoretical literature on factors affecting the decision-making factors of pharmaceutical enterprises and logistics enterprises to ensure drug quality but also provide useful references for improving government policies.