Reliability-based design optimization (RBDO) is receiving more attention from researchers because it can help to minimize cost reasonably in practical engineering. A large number of methods have been proposed to solve RBDO problems, most of which are based on the theory of the first-order reliability method (FORM). Therefore, the deficiencies of the FORM limit applications of general RBDO methods such as the dependency on the minimum performance target point (MPTP). In this study, we apply the fractional moment-based maximum entropy method to the RBDO problems for the first time and propose a novel RBDO method using the quantile-based sequential optimization and reliability assessment method. Because the proposed method is MPTP free, the shortcomings of FORM-based RBDO methods can be overcome. To demonstrate the performance of the proposed method, we test five numerical examples and one engineering example by the proposed method and three popular RBDO methods. The results show that the proposed method can balance the accuracy and the efficiency compared with other methods.