Food safety is an important guarantee for national stability and development. In recent years, with the popularization of mobile networks, the online food delivery industry has flourished. However, due to issues such as the improper management of food delivery businesses and weak regulation, the problem of food safety in the online food delivery industry has become increasingly prominent. This article addresses the situation where both the government and third-party ordering platforms are involved in regulation. It constructs a tripartite evolutionary game model among the food delivery producers, third-party ordering platforms, and government regulatory departments, and analyzes the evolutionary stability of the strategic choices made by each participant. The research findings are as follows: 1) Increasing the incentives and penalties by the government contributes to the production of safe food by the food delivery businesses and encourages the active participation of third-party food delivery platforms in regulation. However, a larger incentive may hinder the government’s own regulatory responsibilities. 2) The government must establish reasonable incentive and penalty mechanisms that ensure the sum of incentives and penalties is greater than the speculative gains of all parties in order to guarantee food safety in the evolving and stable market environment of food delivery. Finally, Matlab 2021a is used for simulation analysis, in order to provide some suggestions for solving the safety problems of takeaway food in our country.