In this study, we consider the issue of sustainable development in the supply chain consisting of an original equipment manufacturer (OEM) and a contract manufacturer (CM). We investigate how to facilitate the CM’s investment in the environmental quality of a product so as to properly respond to climate change. We introduce a quantity incentive contract, and obtain the optimal solution based on a Stackelberg game. The OEM, as the focal company, determines the level of the incentive, and the CM, responsible for product design and production, determines its level of environmental quality given the OEM’s incentive offer. To investigate the effectiveness of the quantity incentive contract and provide important implications, we analytically compare the quantity incentive contract with the basic wholesale price contract without any incentives and conduct numerical experiments. Our results reveal that the quantity incentive contract facilitates the CM’s investment in environmental quality, and enhances the environmental, market, and profit performance of not only the CM but also the OEM which pays the incentive. We also show that the quantity incentive contract is suitable to develop a long-term relationship between the OEM and the CM.