<p>Installing lead rubber bearings (LRBs) is an effective measure to mitigate seismic dynamic responses and ensure the structural safety of girder bridges in near-fault earthquake region. However, accurately determining the parameters of LRBs while considering the random seismic excitation to enhance the seismic isolation and reduction performance is a crucial yet challenging task. In this study, a novel dynamic reliability-based robust design optimization (RBRDO) framework via direct probability integral method (DPIM) is proposed to automatically and efficiently determine the parameters of LRBs for girder bridges subjected to stochastic near-fault ground motions as nonstationary random excitation. Firstly, the optimization formulation is established to minimize the combination of mean and standard deviation of the extreme displacements at pier tops, with the dynamic reliability of LRBs taken as the probabilistic constraint. Then, a versatile and efficient RBRDO approach is developed by combining DPIM devised recently and the method of moving asymptote. The statistical moments, dynamic reliability, and their sensitivities are calculated simultaneously by DPIM. New sensitivity formulas for statistical moments and reliability are derived based on the probability density integral equation, enabling efficient computation without additional structural analysis. Finally, the optimal results demonstrate that the stochastic seismic responses of a continuous girder bridge can be effectively controlled by the optimal design of LRBs. The design scheme confirms the efficacy and superiority of the proposed framework for parameters optimization of LRBs for girder bridges under stochastic near-fault motions. Additionally, the significant effect of velocity pulses on the design of LRBs is revealed.</p>