During strong seismic events, seismic-induced pounding has been observed to cause damage to bridges. Previous studies on seismic-induced bridge pounding responses have generally focused on reinforced concrete bridges. However, the seismic damage between steel and reinforced concrete beams is significantly different, and research on steel beams’ seismic pounding response remains limited. Therefore, this paper adopts the multiscale fine three-dimensional numerical simulation method to study the seismic response of a slab-on-girder steel bridge. The numerical results show that the lower lateral bracing has a significant effect on seismic damage to steel beams. The lower lateral bracing can share about 1/3 of the pounding action and reduce the displacement angle of the steel beam by 40%. Under horizontal two-way seismic action, the lower lateral bracing significantly reduces the stress on the steel beam. In addition, the bracing should have continuous stiffeners to avoid connection failure. Generally, the lower lateral bracing should be considered in the design of the slab-on-girder steel bridge. It significantly improves the lateral seismic performance of the bridge and reduces seismic damage to steel beams.