The objective of structural optimization is to achieve a structural design that produces the best performance while satisfying given design constraints. Despite rapid technological advances in structural optimization, topology optimization of structures under stochastic excitations has not received much attention until recently, primarily due to computational challenges in random vibration analysis. Recently, the authors addressed such technical difficulties by discretizing the stochastic excitations in the standard normal space and performing structural reliability analysis. In this approach, the instantaneous failure probability of the linear system under Gaussian excitations is obtained by a closed-form solution. The research effort helped identify a need to solve system reliability problem in such stochastic topology optimization because the failure event of a structure is often defined as a system event consisting of multiple locations, failure modes and time points. In this paper, a system reliability-based topology optimization method is proposed for structures under stochastic excitations. The proposed method employs the matrix-based system reliability method, which allows for efficient and accurate system reliability analysis and provides the sensitivity of the system failure probability.The proposed method is demonstrated by a numerical example of a structure under stochastic ground motion excitations.