With the sustainable development of the global economy, environmental problems and the green economy are increasingly becoming points of concern for the community. However, the large amount of capital invested in green technology and the high price of green products have become the key problems hindering the development of a risk-averse green supply chain. In order to promote the supply chain to increase green investment level, improve the green degree of products, and reduce the impact of risk aversion on green investment, this paper studies a two-echelon green supply chain composed of a risk-averse manufacturer and a risk-neutral retailer, in which the retailer is the leader and the manufacturer is the follower. We construct the wholesale price contract model, cost-sharing contract model, and two-part contract model, respectively, and use the Optimization Theory and Methods to discuss the impact of the three contracts on the green degree, expected utility of supply chain, retail price, consumer surplus, and social welfare. The results show that in the cost-sharing contract, compared with the wholesale price contract, the green degree of the product has been significantly improved, but the expected utility of the supply chain enterprises cannot achieve Pareto improvement, and the higher consumer environmental awareness will cause the manufacturer’s expected utility to decline. In the two-part tariff contract, compared with the wholesale price contract, the expected utility of supply chain enterprises achieves Pareto improvement, and the green degree of products is the highest in the three contracts; more importantly, in the two-part contract, the product green degree, the retail price, and the expected utility of the supply chain are not related to the manufacturer’s risk aversion; meanwhile, the retail price in the two-part tariff is the lowest among the three contracts, and the consumer surplus and social welfare are the highest. Our main contribution is that the two-part contract eliminates the influence of the manufacturer’s risk aversion on the above decision variable and realizes the unification of manufacturers, retailers, consumers, and social benefits. Finally, this paper uses numerical examples to verify the above conclusions and then analyzes the sensitivity of the supply chain system.