Abstract: For the green supply chain consisting of a manufacturer and a retailer while consumers are sensitive to the price and greenness of green products, an investigation is conducted into how the government's incentive policy affects the manufacturer's decision-making about green products' greenness and supply chain coordination mechanism. A vertical game model under centralized decision-making and manufacturer-led Stackelberg game model under decentralized decision-making is established to get the optimal price, greenness and profits of every organization. Then, cost-sharing or revenue sharing contracts are proposed to coordinate the supply chain. The above conclusions are verified through a numerical analysis and the parameters sensitivity analysis is carried out. The study indicates that: compared with decentralized decision-making, under centralized decision, the greater the green degree is, the lower the retail price is and the higher the overall profits of the supply chain are; and a single cost-sharing contract cannot achieve supply chain coordination; and for the revenue sharing contracts combined with cost sharing, the ratio of revenue sharing is negatively related to the ratio of cost sharing; the profits of each member are positively correlated with the adjustment factors of government subsidies and the coefficient of greenness sensitivity but negatively correlated with coefficients of the price sensitivity and the green investment.