This paper considers a two-stage supply chain with the loss-adverse retailer, among which the demand and market price fluctuate randomly with emergencies. Then the models of centralized and decentralized systems are constructed under the emergency quantity flexibility contract, and the equilibrium solutions of supply chain under emergencies are obtained. Also, the influence of flexibility range, wholesale price and loss aversion extent on retailers' optimal ordering decision and supply chain members' profits is discussed . The results show that the supply chain can be coordinated if the flexibility range and the wholesale price are adjusted within the reasonable section. Finally, the numerical examples verifies the correctness of the conclusion.