This paper considers inventory problems for perishable or deteriorating products to maximize the total profit considering high- and low-priority customers based on the conditional Value-at-Risk (cVaR). The cVaR is a useful risk measure in economics and finance, which satisfies all requirements of ideal risk measures such as coherence and stochastic dominance. In order to apply random sampling derived from known distributions or historical data to our proposed model and to develop an analytical and efficient solution algorithm, the scenario-based solution algorithm is developed by performing equivalent transformations into a linear programming problem. Furthermore, numerical examples are provided to compare our proposed model with the previous standard model based on the expected value for the total profit. Furthermore, the results also show differences from the previous cVaR-based model with only one demand under some random distributions.