Sandwich structure with honeycomb core and CFRP facesheets is increasingly used in the high-performance fields due to the high specific stiffness and strength. However, it is susceptible to localized low-velocity impacts such as tool drop during maintenance, and thus, understanding the damage behavior is important for a safety design and optimization. The objective of this article is to investigate the influence of the structural parameters and impact energy on the damage behaviors of the composite honeycomb sandwich panels subjected to localized low-velocity impact. An effective computational framework considering complicate damage mechanisms is proposed to predict the failure patterns, load history, and energy absorption. Comparisons with the experimental data show that the error of predictions is within 4% and thus the framework is validated. Then, a comprehensive parametric study is conducted to explore the effects of wall thickness and height of honeycomb, impact energy, and stacking sequences of the laminated facesheets on the impact resistance, damage behaviors, and energy absorption of the sandwich structure. The reported results may be useful in practice.