With the increase of public environmental awareness and the growth of e-commerce, sustainable development promotes the manufacturer to increasingly participate in green innovation and make full use of the online sales channel to enhance competitiveness. Despite decentralized encroachment being widely adopted in business reality, the current literature has commonly paid more attention to centralized encroachment. To complement related research, a dual-channel green supply chain composed of a manufacturer (its retail subsidiary) and a retailer is investigated. We focus on what encroachment strategy (centralization vs. decentralization) drives the green innovation and analyze the impact of consumer green awareness and product substitutability on the manufacturer’s encroachment strategy, green innovation efforts and supply chain performance. Under each encroachment strategy, we build a Stackelberg game model and derive the equilibrium outcome. Then, we theoretically analyze the effects of consumer green awareness and product substitutability on green innovation and each party’s profitability. Our comparative analysis shows what encroachment strategy drives green innovation and what encroachment strategy benefits both parties and social welfare. Numerical studies are also conducted to support the analytical results. Our key findings reveal that decentralization improves the green innovation and achieves a both-win situation for the manufacturer and the retailer. Besides that, decentralization can reduce the environmental damage and increase social welfare as well.