The green market is a typical information asymmetric market, hence enterprises need to use eco-labels to communicate the environmental quality information of their products to consumers. We consider voluntary corporate self-labeling and government certified-labeling, and focus on a retail channel green supply chain consisting of the government, a manufacturer, and a retailer, in which the government implements environmental regulations, the manufacturer produces two types of green products, and the retailer has private market information. This paper aims to explore the eco-label selection strategy of stakeholders for two green products under the joint influence of government financial intervention and retailer information sharing. Using game theory and mathematical programming methods, we obtain the optimal prices, greenness, and taxes of products with different information arrangements of the retailer under the two eco-label strategies. Through the analysis of the results, we find that the government provides subsidies for green products, and the subsidy of the marginal cost-intensive green product (MIGP) in the certified-labeling is always higher than that of the self-labeling, while the subsidy of the development-intensive green product (DIGP) in the certified-labeling is not always higher than that of the self-labeling. The supply chain distortion caused by information asymmetry does not affect the greenness decision of MIGP in the self-labeling, but it does change the greenness level design of DIGP. Moreover, the retailer's information sharing strategy affects the label choice of the DIGP manufacturer, but it does not change the label preferences of participants in the MIGP supply chain. These findings contribute to the development of tailored strategies of the manufacturer and the retailer for different products, as well as the establishment of the government eco-label schemes.