A high spike force at the beginning of impact and the load fluctuations caused by unstable plateau deformation are disadvantages to avoid for impact resistance structures. Lightweight glass fiber-reinforced polypropylene composite hierarchical cylindrical structures (namely GFRP-CHCS, with a relative density of less than 0.1) have the potential to achieve low initial force and high crushing force efficiency under dynamic conditions. This work explores the drop-weight impact behaviors and energy absorption capacity of GFRP-CHCS. Deformation modes, failure conditions, and impact load history responses are discussed. Results showed that GFRP-CHCS has no initial load peak and achieves gentle response curves under the low-velocity impact when the load speed is less than 10 m/s. Among the experiments where the impact energy was beyond the range of static energy absorption, more than 94% of the impact energy was absorbed or dissipated when the impact energy ranged from 200 J to 300 J. After unloaded, GFRP-CHCS maintained good integrality and recovered a significant deformation which was over 93% initial structural height. With ideal isotropic material properties, numerical and theoretical predictions were conducted regarding the loading velocity effects on structural deformation mode and mean impact response force. This work utilized a thermoplastic composite consisting of GFRP face sheets and polypropylene core. The results have reference significance for the anti-impact design of thermoplastic composite hierarchical structures.