The low efficiency of the closed-loop supply chain in construction and demolition waste (CDW) recycling has restricted the green development of China’s construction industry. Additionally, the government’s reward–penalty mechanism has a huge influence on green development. This study aimed to investigate the effect of green development performance (GDP) and the government’s reward–penalty mechanism on the decision-making process of production and recycling units, as well as to reveal the optimal strategies under different conditions. Therefore, the strategies’ evolutionary paths of production and recycling units were investigated by using evolutionary game theory. Firstly, an evolutionary game model between production units and recycling units was proposed under the government’s reward–penalty mechanism. Then, the evolutionary stability strategies in different scenarios were discussed. Finally, the effects of the relevant parameters on the evolutionary paths of the game model were analyzed using numerical simulations. The main conclusions are as follows. (1) When the range of GDP changes, the evolutionary stable strategy changes accordingly. GDP plays a positive role in promoting the high-quality development of the CDW recycling supply chain, but an increase in GDP can easily lead to the simultaneous motivation of free-riding. (2) The government’s reward–penalty mechanism effectively regulates the decision-making process of production and recycling units. An increase in the subsidy rate and supervision probability helps to reduce free-riding behavior. Moreover, the incentive effect of the subsidy probability on recycling units is more obvious, while the effect of the supervision probability on improving the motivation of active participation for production units is more remarkable. This paper not only provides a decision-making basis to ensure production and recycling units to make optimal strategy choices under different conditions but also provides a reference for the government to formulate a reasonable reward–penalty mechanism that is conducive to a macro-control market.