Origami offers a novel design possibility for periodic sandwich cores. The curved-crease origami is adopted to enhance the anti-buckling performance and reduce the abrupt change of the carbon fibers in the origami sandwich cores. CFRP curved-crease origami sandwich structures were fabricated using a hot press molding method. Analytical models were developed for predicting the shear stiffness and strength concerning different failure modes including debonding, compressive and shear buckling, tensile, compressive and shear fracture in both transverse and longitudinal directions. The shear deformation histories, failure modes, strength and stiffness of the sandwich structures were investigated through experiments and finite element analysis (FEA). The analytical models, experiments, and simulations agree with each other reasonably. The origami sandwich undergoes buckling failure when the wall thickness of the origami core is sufficiently thin. With the increase of the wall thickness, debonding between the face sheets and the origami cores usually occurs instead of fracture. The exploration of the shear behaviors lays the foundation for the applications of the origami sandwich structures in the lightweight construction fields.