Due to the increasing awareness of sustainable manufacturing, remanufacturing has been widely accepted by enterprises in many countries. In the process of Closed-Loop Supply Chain (CLSC) development, to stimulate the demand for remanufactured products, the Chinese government’s interventions such as the “Trade old for Remanufactured” program cannot be ignored. However, prior research has not answered the questions of whether governments should offer consumption subsidies and how to determine the optimal subsidy value. This paper investigates the optimal government consumption subsidy policy and its impact on the operation of Closed-Loop Supply Chain (CLSC) where an Original Equipment Manufacturer (OEM) produces new products, while a Third-Party Remanufacturer (TPR) remanufactures the used products collected from consumers. A game model with a leader (government) and two followers (OEM and TPR) is then introduced. The government determines the consumption subsidy to maximize the social welfare, while the TPR and OEM attempt to maximize their own profit functions. Game theoretic models are proposed to explore and compare the scenarios, i.e., CLSC with a consumption subsidy policy and without a consumption subsidy policy. The equilibrium characteristics with respect to the government’s consumption subsidy decisions and the price decisions for chain members are derived. Based on the theoretical and numerical analysis, the results show that: (1) governments should not always offer a consumption subsidy; (2) the consumption subsidy cannibalizes demand for new products while boosting the demand for remanufactured products; (3) the consumption subsidy should be shared between the TPR and consumers when the TPR raises the sales price of remanufactured product; (4) the members of the CLSC do not always benefit from the consumption subsidy policy.