Considering a dual channel supply chain based on differential game involving a green manufacturer and a retailer, the paper studies the optimal equilibrium strategies and profits in centralized supply chains, and decentralized supply chains with the competitive advertising strategy and the supportive advertising strategy respectively. The analytic results show that the optimal low-carbon level, optimal online and offline advertising level in the centralized model are higher than that in the decentralized model, while the optimal sale price maybe higher, equal or lower than the that in the decentralized model. In the decentralized model, the optimal low-carbon level, optimal sale price and optimal online advertising level of the dual-channel supply chain with the supportive advertising strategy are consistent in the optimal strategies of the dual-channel supply chain with the competitive advertising strategy. It also suggested that the supportive advertising strategy enables the dual channel supply chain to achieve Pareto improvement, while the optimal offline advertising level under the supportive advertising strategy is greater than that under the competitive advertising strategy on the mean time.