This study develops an efficient and accurate methodology for reliability-based design optimization (RBDO) by combining the most probable point (MPP)-based dimension reduction method (DRM) to enhance accuracy and the sequential optimization and reliability assessment (SORA) to enhance efficiency. In many researches, first-order reliability method (FORM) has been utilized for RBDO methods due to its efficiency and simplicity. However, it might not be accurate enough for highly nonlinear performance functions. Therefore, the MPP-based DRM is introduced for the accurate reliability assessment in this study. Even though the MPP-based DRM significantly improves the accuracy, additional computations for the moment-based integration are required. It is desirable to reduce the number of reliability analyses in the RBDO process. Since decoupled approaches such as SORA reduce necessary reliability analyses considerably, DRM-based SORA is proposed in this study for accurate and efficient RBDO. Furthermore, convex linearization is introduced to approximate inactive probabilistic constraints to additionally improve the efficiency. The efficiency and accuracy of the proposed method are verified through numerical examples.