This paper documents the first attempt to apply the differential game theory for investigating some properties of a low-carbon supply chain coordination by employing the cost-sharing mechanism. The manufacturer is the brand owner and the corresponding low-carbon goodwill is increased with respect to the reference emission reduction effect and consumption promotion. Three dynamic games are well-studied by considering the multiple effects of price and non-price factors on the market. It can be observed that the manufacturer always prefers to employ the coordination mechanism. When the manufacturer opts for a cost-sharing program, the manufacturer and retailer under Model-D are always economically better off, and therefore a cost-sharing program is always profit-Pareto-improving.