With the aid of differential game, the vertical joint promotion problem of a supply chain consisted of a single manufacturer and two competitive retailers is studied, in which the goodwill is used as a state variable. In the case that the demand of products is affected by goodwill and retailers' promotion, centralized and decentralized differential game models are constructed. The cost-sharing contract is introduced to coordinate the supply chain. Furthermore, the sensitivity analysis of related parameters is conducted by using the numerical simulation method. It is found that, by introducing the cost-sharing contract, the promotion effort, the goodwill and the demand of products are promoted. The coordination of the supply chain is achieved. Meanwhile, with the increasing of the retailers' competition degree and the cost coefficient of promotion effort, the added profit of the supply chain members with the contract presents a declining curve. On the contrary, with the increasing influence of retailers' promotion effort and the goodwill on the demand, the added profit of the supply chain members with the contract is on the risen.