The most attractive structural feature of the three-dimensional (3D) angle-interlock woven structure is that the straight weft yarns are bundled by the undulated warp yarns, which induces the overall good structural stability and a stable fabric structure. Thus the 3-D angle-interlock woven composite (3DAWC) prepared by the vacuum-assisted resin transfer molding (VARTM) curing process has excellent mechanical properties by using the fabric and epoxy resin as the reinforcement and matrix, respectively. The low-velocity impact damage properties of the composites under different drop-weight energies (70, 80, and 100 J) were tested experimentally. The load–displacement curves, energy–time curves, and the ultimate failure modes were obtained to analyze the performance of resistance to low-velocity impact, as well as the impact energy absorption effect and failure mechanism, especially the structural damage characteristics of the 3DAWC subjected to the low-velocity impact of drop weight. By analyzing the obtained experimental results, it is found that the fabric reinforcement is the primary energy absorption component and the impact energy mainly propagates along the longitudinal direction of the yarns, especially the weft yarn system, which is arranged in a straight way. In addition, as the impact energy increases, the energy absorbed and dissipated by the composite increases simultaneously. This phenomenon is manifested in the severity of deformation and damage of the material, i.e., the amount of deformation and size of the damaged area.