Origami has emerged as a promising tool for the design of mechanical structures that can be folded into small volume and expanded to large structures, which enables the desirable features of compact storage and effective deployment. Most attention to date on origami deployment has been on its geometry, kinematics, and quasi-static mechanics, while the dynamics of deployment has not been systematically studied. On the other hand, deployment dynamics could be important in many applications, especially in high speed operation and low damping conditions. This research investigates the dynamic characteristics of the deploying process of origami structures through investigating a Miura-Ori sheet (Fig. 1(b, c)). In this study, we have utilized the stored energy in pre-deformed spring elements to actuate the deployment. We theoretically model and numerically analyze the deploying process of the origami sheet. Specifically, the sheet is modeled by bar-and-hinge blocks, in which the facet and crease stiffnesses are modeled to be related to the bar axial deformation and torsional motion at the creases. On the other hand, the structural inertia is modelled as mass points assigned at hinges. Numerical simulations show that, apart from axial contraction and expansion, the origami structure can exhibit transverse motion during the deploying process. Further investigation reveals that the transverse motion has close relationship with the controlled deploying rate. This research will pave the way for further analysis and applications of the dynamics of origami-based structures.