Core panels inspired by origami have the advantages of force allocation and energy dissipation. Used as a sandwich core, the three-dimensional panels could be created using various origami patterns. The panel is composed of the element whose structure is inspired by origami. The orthopyramid-like origami element has a tip of joined-together side triangles. Through shape deformation, it could exhibit potential mechanical performances. Owing to its deformation when collision occurs, the structure could be employed for load damping conditions. This study focuses on nine different orthopyramid-like core panels through changing the similarity parameter value and the number of edges. The experiment and numerical simulation of compression and impact tests are carried out to perform the parametric study on the influences of the similarity parameter and the number of edges. The results show that with the increase of these two parameters, the panel tends to be softer, greatly influencing the load damping ability. Moreover, the structure parameters are optimized by the Genetic Algorithm integrated with the finite element analysis model.