Because of the uncertainty of the market, there exist some risks in the sales volume of the retailers. So that retailers can feel regretful which can influence their decisions. Therefore, this article investigated the coordination of the supply chain that consisted of single rational supplier and single regret aversion retailer under the circumstances where the market demand was uncertain via buy-back contract. And a numerical analysis was conducted to explore the impact of the retailer’s risk aversion on its optimal order quantity and the optimal buy-back price of the supply chain. The result showed that after taking the regret aversion of the retailer into consideration, if parameters were assigned properly, the buy-back contract would be able to coordinate the supply chain. The impact of the regret coefficients on the retailer's optimal order quantity and the optimal buy-back price of the supply chain relied on the retailer’s preference for surplus regret and shortage regret.