Green design by manufacturers is essential for achieving supply chain sustainability, and large retailers may exhibit altruistic preferences to incentivize such efforts. Accordingly, this study develops three game-theoretic models of a two-echelon supply chain composed of a manufacturer and a dominant retailer, with and without altruistic preferences, to examine how altruism and green design affect firms’ optimal decisions and environmental impact. In addition, two coordination mechanisms—green design cost-sharing and two-part tariff contracts—are proposed under altruistic preferences. We find that the dominant retailer’s altruistic preference can motivate the manufacturer to improve the green design level and increase system profit. Although the dominant retailer has altruistic preference, they cannot always lower the total environmental impact of products, so it is helpful to motivate the manufacturer to reduce the environmental adverse impact by increasing investments in green design. Both the two contracts designed in this paper can achieve incentive compatibility and perfect coordination of supply chain. However, with the retailer’s altruistic preference enhancement, the feasible range of the two contracts will be reduced.