Managing quality risks of prefabricated components is one of the challenges for prefabricated construction. The quality liability insurance for prefabricated components (QLIPC) is an effective approach to transfer such risks; however, limited research has been conducted on the development of QLIPC. This study introduces an evolutionary game theory (EGT)-based approach incorporating decisions from both government and insurance companies. In the EGT model, a payoff matrix under disparate strategies is constructed and the evolutionary stable strategies (ESS) are deduced. The simulation calculation is then carried out by MATLAB using virtual sample data to demonstrate the analysis. The results show that the government should act as the game promoter because the QLIPC can reduce governance cost and has significant social benefits. This research contributes a theoretical framework to analyze the QLIPC development using the EGT theory, and it could help the government develop long-term strategies for developing the QLIPC market.