Thick-panel origami has shown great potential in engineering applications. However, the thick-panel origami created by current design methods cannot be readily adopted to structural applications due to the inefficient manufacturing methods. Here, we report a design and manufacturing strategy for creating thick-panel origami structures with excellent foldability and capability of withstanding cyclic loading. We directly print thick-panel origami through a single fused deposition modeling (FDM) multimaterial 3D printer following a wrapping-based fabrication strategy where the rigid panels are wrapped and connected by highly stretchable soft parts. Through stacking two thick-panel origami panels into a predetermined configuration, we develop a 3D self-locking thick-panel origami structure that deforms by following a push-to-pull mode enabling the origami structure to support a load over 11000 times of its own weight and sustain more than 100 cycles of 40% compressive strain. After optimizing geometric parameters through a self-built theoretical model, we demonstrate that the mechanical response of the self-locking thick-panel origami structure is highly programmable, and such multi-layer origami structure can have a substantially improved impact energy absorption for various structural applications.