Traditionally, origami-based structures are designed on the premise of "rigid folding," i.e., the facets and fold lines of origami can be replaced with rigid panels and ideal hinges, respectively. Miura-ori and double corrugation surface are representative rigid-foldable origami models. However, from a structural mechanics viewpoint, these systems are usually overconstrained and have negative degrees of freedom (DOF), i.e., the number of constraints exceeds the number of variables. In these cases, the singularity in crease patterns guarantees their rigid foldability. Further, if misalignments are included in the systems' crease patterns, they become no longer rigid-foldable. This study presents a new method for designing self-deploying origami using the geometrically misaligned creases. In this method, some facets are replaced by "holes" such that the systems become a 1-DOF mechanism. These perforated origami models can be folded and unfolded similar to rigidfoldable (without misalignment) models because of their DOF. Focusing on the removed facets, the holes will deform according to the motion of the frame of the remaining parts. In the proposed method, these holes are filled with elastic parts and store elastic energy for self-deployment. First, a new extended rigid-folding simulation technique is proposed to estimate the deformation of the holes. Next by using the above technique, the proposed method is applied on arbitrary-size quadrilateral mesh origami. Finally, by using the finite-element method, the authors conduct numerical simulations and confirm the deployment capabilities of the models.