In this paper, the optimization of single-period inventory problem under uncertainty is analyzed. Due to lack of historical data, the demand is subjectively determined and represented by a fuzzy distribution. Uncertain demand causes an uncertain total cost function. This paper intends to find an analytical method for determining the exact expected value of total cost function for a fuzzy single-period inventory problem. To determine the optimum order quantity that minimizes the fuzzy total cost function we use the expected value of a fuzzy function based on credibility theory. The closed-form solutions to the optimum order quantities and corresponding total cost values are derived. Numerical illustrations are presented to demonstrate the validity of the proposed method and to analyze the effects of model parameters on optimum order quantity and optimum cost value. The proposed methodology is applicable to other inventory models under uncertainty.