Smart government is an important means of optimizing government management, improving the government decision-making capacity, and pushing forward the public service. When the smart government process applies, the dire straits of collaborative governance among the different participants could not be ignored usually caused by maximizing their profits. Based on the current research, this paper introduces the blockchain technology into the smart government system and establishes a smart government platform architecture. Meanwhile, to analyse the evolutionary and stable strategies of the three parties under the blockchain technology, the evolutionary game model including functional departments, local governments, and end users as the main players is established on account of the bounded rationality. By examining the “blockchain + government service” in Beijing with the systemic dynamics theory, this paper changes the influencing factors simulated by changing the parameter assignment, to determine the evolutionary stable equilibrium under different external conditions. The results show that local government supervision plays a leading role in the process of collaborative governance of smart government based on blockchain technology; meanwhile, effective cost control is a key factor affecting the evolutionary stability strategy (ESS). Besides, the “decentralized” structure, “distrust” architecture, and “precision” mechanism of the blockchain are verified for the effect of the evolution process. Among them, precision service and flat management improve the possibility of collaborative governance, but the impact of the trust mechanism is not obvious. Therefore, the collaborative governance model of smart government based on blockchain technology is loaded with far-reaching significance for promoting the modernization of China’s governance capacity and governance system.