Reliability-based design optimization (RBDO) draws more and more attention because minimizing cost reasonably is anticipated 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). This paper proposes a novel RBDO method with the aid of the quantile-based sequential optimization and reliability assessment method, in which the fractional moment-based maximum entropy method is applied to RBDO problems for the first time. Because the proposed method is MPTP-free, the shortcomings of FORM based RBDO methods can be overcome. For demonstrating the performance of the proposed method, five numerical examples and one engineering example are tested by three popular RBDO methods and the proposed method. The results show that the proposed method can achieve the tradeoff of the accuracy and the efficiency compared with other methods.