Logistics channel is the lifeblood to ensure that logistics serves the circulation inside and outside the region, and to realize regional economic integration, it greatly contributes to the implementation of the national unified market strategy. As the government plays an important role in the construction of logistics channels, this paper further clarifies the effect of government participation and support policies by defining the role and functions of the government in the construction of logistics channels. Based on the evolutionary game theory, the paper reveals the equilibrium conditions of logistics channel construction under the market mechanism and government guidance under the assumption of bounded rationality. We construct an evolutionary game model among participating stakeholders, then study the evolutionary stability strategy of logistics channel participation behavior using the stability theorem for the model’s differential equations. In order to explore the dynamic evolution process of both parties’ choices under the two modes, we investigates the influence of the initial intention, cooperative income, cost proportion, penalty coefficient and construction cost of participating enterprises on both parties’ strategic decisions under the market mechanism and government guidance modes through numerical simulation. We find that: (1) under the market mechanism and government guidance modes, there is a game equilibrium in the participation behavior of logistics enterprises in the national unified market, and that the conditions for realizing the equilibrium of cooperation among stakeholders under the guidance of the government are easier to meet; (2) The initial intentions of the two players in the game along the logistics channel influence each other, and government participation can change the effects of cooperative income, the penalty coefficient and construction cost on the system game strategy, which has a positive effect on the channel construction; (3) At the same time the simulation shows that the government’s promotion effect has certain limitations, and the government should provide reasonable guidance to prevent enterprises from hindering the healthy development of logistics channels. This study provides a theoretical reference for the government and logistics enterprises, especially relying on logistics channels to support the regional coordination of national unified market development.