The increased risk of vehicle collisions on bridge piers causes damage to bridge structures and traffic congestion. In extreme cases, severe collisions caused by trucks lead to bridge collapse and loss of lives. Many studies have been conducted to investigate the dynamic responses of bridge piers subjected to vehicle collisions. Most of them focused on head-on (center-to-center) collisions based on the assumption that they represented the worst scenarios. However, off-center collisions were most often observed in vehicle collision accidents. In this study, bridge piers with different cross-section geometries (i.e., circular, and square) subjected to off-center vehicle collisions are numerically investigated. The results show that off-center vehicle collisions result in more severe spalling damage to the circular piers than head-on collisions. However, the curved surface of the circular piers effectively avoids inducing torsional response under off-center collisions. On the other hand, off-center collisions on square piers induce torsional response, thus more significant deformation, and damage than head-on collisions. Further mechanism analyses are conducted to explain the influence of off-center collisions, focusing on truck type and rectangular cross-section. Furthermore, some meaningful suggestions are put forward to resist off-center vehicle collisions for bridge piers in design process or in service.