Coordinating supply chains has been a major issue in supply chain management research. This paper focuses on the coordination of supply chains with downside-risk-averse agents. Motivating by the revenue sharing contract, we developed the sufficient conditions for the coordination of the supply chain with one downside-risk-averse agent. Following the sufficient conditions, the downside protection contract thus developed also allows arbitrary allocation of the profit between the supplier and the retailer. We also develop the necessary condition for the coordination of the supply chain when both the supplier and the retailer are downside-risk averse. We hope this work sheds some insights to the study of the coordination of supply chains with downside-risk-averse agents in more general situations.