Based on the condition of Corporate Social Responsibility (CSR), we address a supply chain composed of a manufacturer and a CSR retailer considering three cases:centralized one, decentralized one, and decentralized one with Revenue Sharing (RS) contract.The research results show that, the optimal profit of the centralized supply chain decreases with the CSR level.In the decentralized case, the retailer's profit decreases and the manufacturer's profit increases along with the increase of retailer's CSR level.While in the decentralized case with RS contract, the RS coefficient affects the retailer's optimal profit, specifically, the retailer's profit decreases along with the increase of its CSR level when the RS coefficient is within certain range, while out of that range, the retailer's profit would increase along with the increase of its CSR level;however, the manufacturer's profit always increases with retailer's CSR level.The social welfare increases along with the retailer's CSR level when the CSR level is relatively low, then it would decrease with the retailer's CSR level when the CSR level is relatively high.In the end, we provide a numerical example and derive some managerial implications.