With the acceleration of aging in China, the scale of disabled and semi-disabled people has expanded, and the demand for long-term care has sharply increased. The long-term care insurance system has covered 49 pilot cities in China since pilots were launched in 2016. In view of the interest game between different groups in the pilot of long-term care insurance system, an evolutionary game model of local government and long-term care insurance service institutions was constructed based on evolutionary game theory, the evolutionary process of the strategy selection of long-term care insurance service institutions and the government was studied, and the evolutionary stability strategies of both parties were analyzed. On this basis, the simulation results showed that rent-seeking behavior of long-term care insurance service institutions, government policy adjustment and punishment will affect the strategic choices of long-term care insurance service institutions and the government. Both sides should improve the constraint mechanism as soon as possible, establish a benign relationship of equality and mutual benefit. Therefore, we suggest that the government optimize policy content, enhance the regulation, improve construction of institutional system, promote active cooperation between long-term care insurance service institutions and the government, and promote the continuous improvement of the long-term care insurance system.