A folding fabrication method inspired by origami for carbon fiber-reinforced composites to fabricate three-dimensional structures is presented. PMI foams serve as substrates, making it possible to manufacture this kind of origami-inspired composite sandwich materials in a single-step process. Analytical models are proposed to provide upper and lower bounds of the out-of-plane compressive strength of the origami-inspired composite sandwich materials. Finite element analysis (FEA) and experiments are conducted to characterize the compressive behaviors including the deformation history, failure mode, strength, etc., and verify the validity of the analytical models. By incorporating PMI foams, the out-of-plane compressive failure mode of the composite sandwich material at low relative density changes from buckling to wrinkling or crushing, thus greatly increasing the strength. Additionally, the energy absorption capacity is significantly enhanced due to the PMI foams and their interaction with the composite origami core. This work creates a new method to fold composites into lightweight sandwich materials with high strength and high energy absorption, paving the way for their applications in transport, energy and communication.