To enhance the seismic mitigation performance of conventional damped outrigger （CDO） system， this study investi? gates the seismic performance improvement of inerter-negative stiffness damped outrigger （INSDO） system， which is based on the three-element passive mitigation system consisted of inerter， stiffness and damper. The Clough-Penzien spectrum model is adopted to simulate stationary stochastic seismic excitation， and the motion equations of the structure-damper-excitation system are then ex? pressed utilizing augmented state space method. The root-mean-square （RMS） of the structural response under stochastic excita? tion is calculated via the solution of Lyapunov equation， and optimal parameters of INSDO system are determined by multi-objec? tive optimization method based on maximum harmful inter-story drift and acceleration control. The seismic performance of INSDO system under typical natural seismic records is further evaluated. Results indicate that compared with the CDO system， the opti? mum INSDO system can reduce the bottom average story drift RMS by 57.97% and the top average absolute acceleration RMS by 36.99% under El-Centro and Kobe excitations， which further verifies the effectiveness of multi-objective optimization method. Compared to the introduction of inerter or negative stiffness element alone， the combination of two kinds of element can further am? plify the displacement of the damping element， and realize the seismic performance enhancement of INSDO system by improving the energy dissipation ratio of damper and seismic input energy.