The experimental and numerical investigations on the dynamic responses and failure mechanisms of honeycomb panels under low-velocity impact were carried out in the present work. The carbon fiber composite hexagonal honeycomb panels were fabricated using the hot press molding method. Then, low-velocity drop-weight impact tests on the composite honeycomb panels were conducted under impact energy levels of 5J, 10J, 30J, 50J, 60J, 70J, and 100J to study the deformation mechanisms and damage modes. The VUMAT was developed to model the behavior of sandwich panels, in which a progressive damage model based on the strain-based failure criterion of composite fabric and Yeh delamination failure criteria was implemented in ABAQUS/Explicit. Two-dimensional topological honeycomb configurations with the same relative density were established. The energy absorption and load-bearing capacity of hexagonal, square, triangular, Kagome, and two kinds of circular (CS and CH types) honeycombs under 100J impact energy were discussed. The results showed that the circular honeycomb (CH type) had the largest first peak force of 6.714 kN, while the hexagonal honeycomb had the smallest first peak force of 3.715 kN. Compared with hexagonal honeycomb, the energy absorption of the triangle, Kagome, and circular honeycombs (CH type) were increased by 37.15%, 38.18%, and 47.06%, respectively. This study provided a series of experimental and numerical results, which could provide a reference for selecting suitable honeycomb configurations in the protection field.