In structural design, reliability-based design optimization (RBDO) has been applied to obtain a set of design variables that maximize/minimize the given objective function and satisfy given constraints. In many previous studies, the objective function and constraints were formulated for component events, which represent the failure of structural members. However, a structure often has structural redundancy. For example, when a structure is subjected to cyclic loading, local fatigue-induced failures may initiate sequential failures, which may lead to structural collapse. Therefore, for the RBDO of such a structural system, it is essential to consider the risk of fatigue-induced sequential failure at a system level. To quantify the likelihood of fatigue-induced sequential failures and identify critical failure sequences, the Branch-and-Bound method employing system reliability Bounds (termed the B3 method) was recently developed. This method identifies critical sequences of fatigue-induced failures in the decreasing order of their likelihood, and the method was successfully demonstrated through its application to several types of structural systems. This paper proposes a new RBDO approach that considers structural redundancy against fatigue-induced failure. To properly consider fatigue-induced sequential failure, the proposed approach employs the B3 method and obtains system-level probabilities and sensitivities, which are required for the RBDO of structural systems. The proposed approach is tested and demonstrated by using a simple numerical example.