Reliability-based design optimization (RBDO) of the NASA stage 37 axial compressor is performed using an uncertainty model for stall margin in order to guarantee stable operation of the compressor. The main characteristics of RBDO for the axial compressor are summarized as follows: First, the values of mass flow rate and pressure ratio in stall margin calculation are defined as statistical models with normal distribution for consideration of the uncertainty in stall margin. Second, Monte Carlo Simulation is used in the RBDO process to calculate failure probability of stall margin accurately. Third, an approximation model that is constructed by an artificial neural network is adopted to reduce the time cost of RBDO. The present method is applied to the NASA stage 37 compressor to improve the reliability of stall margin with both maximized efficiency and minimized weight. The RBDO result is compared with the deterministic optimization (DO) result which does not include an uncertainty model. In the DO case, stall margin is slightly higher than the reference value of the required constraint, but the probability of stall is 43%. This is unacceptable risk for an aircraft engine, which requires absolutely stable operation in flight. However, stall margin obtained in RBDO is 2.7% higher than the reference value, and the probability of success increases to 95% with the improved efficiency and weight. Therefore, RBDO of the axial compressor for aircraft engine can be a reliable design optimization method through consideration of unexpected disturbance of the flow conditions.