Anti-roll and anti-pitch are important directions in the comprehensive research of automobiles. In order to improve the anti-roll and anti-pitch performance of the vehicle, an inerter was applied to the vehicle suspension system, and a 14 DOF vehicle nonlinear dynamics model was established. The influence of the change in inertance in the eight kinds of improved ISD (Inerter-Spring-Damper) suspension structures on the RMS (root mean square) value of performance indexes of roll, vertical, and pitch motion of the vehicle was studied. Based on this, the vehicle’s ISD structure with better performance was selected, and the NSGA-Ⅱ algorithm was adopted to optimize the selected structural parameters. The simulation results showed that the four kinds of suspension hadbetter comprehensive performance, and their structureswere, respectively, excluding the supporting spring in parallel, (1) an inerter in series with a spring and a damper in parallel, (2) a damper in series with a spring and an inerter in parallel, (3) an inerter and a damper in series, and (4) the damper in parallel with a spring and an inerter in series. The ISD suspension structure had better comprehensive performance under step steering braking, which was obviously better than the passive suspension, and effectively improved the vehicle ride comfort, anti-roll and anti-pitch performance. Under the hook steering braking, the lateral load transfer rate was used to evaluate the vehicle’s anti-rollover ability. The results showed that the ride comfort and anti-rollover ability of ISD suspension were better than those of passive suspension. Under the condition of taking into account the anti-pitching ability, the suspension consists of a supporting spring in parallel with an inerter, and a damper in series was better.