In this paper, a novel metamaterial fabricated by origami methods is proposed. The quasi-static compression tests and numerical simulations are carried out to explore its deformation mechanisms and energy absorption performances. The numerical results agree well with the experimental results. The effects of the geometrical parameters and load conditions including the wall thickness, load velocity, opening radius and fold number on the energy absorption capacity and crush response are discussed. Finally, the sequential response surface method (SRSM) is applied to solve a structural optimization problem and find the optimal design. Results show that the deformation modes with bending and unfolding of the unit cells contribute to energy dissipation. Increasing the wall thickness and load velocity can raise the specific energy absorption (SEA) and the initial peak crushing force (PCF) level substantially. Introducing the horizontal opening, the SEA and mean crushing force (MCF) level can be enhanced, while the SEA and MCF level are decreased when the openings are introduced in the vertical direction or both horizontal and vertical directions. The structures which increase fold numbers in the two orthogonal directions exhibit better energy absorption and impact resistance capacities. Based on the surrogate optimization, the SEA level of the structure is increased by 10.04% compared with the original design.