Carbon dioxide capture and utilization (CCU) technology is a significant means by which China can achieve its ambitious carbon neutrality goal. It is necessary to explore the behavioral strategies of relevant companies in adopting CCU technology. In this paper, an evolutionary game model is established in order to analyze the interaction process and evolution direction of local governments and coal-fired power plants. We develop a replicator dynamic system and analyze the stability of the system under different conditions. Based on numerical simulation, we analyze the impact of key parameters on the strategies of stakeholders. The simulation results show that the unit prices of hydrogen and carbon dioxide derivatives have the most significant impact: when the unit price of hydrogen decreases to 15.9 RMB/kg or the unit price of carbon dioxide derivatives increases to 3.4 RMB/kg, the evolutionary stabilization strategy of the system changes and power plants shift to adopt CCU technology. The results of this paper suggest that local governments should provide relevant support policies and incentives for CCU technology deployment, as well as focusing on the synergistic development of CCU technology and renewable energy hydrogen production technology.