Abstract: Due to the advantages of large storage ratio, high controllability, reconfigurability, easy assembly and diversified design, the origami structure has broad application prospects in the fields of aerospace, biomedicine, architecture, robotics, material science, etc. With the development of origami structure engineering, the dynamic research for the origami structure with low stiffness becomes more important. In this paper, a general bar-and-hinge dynamics model is developed, in which a non-rigid origami structure is equivalent to a spatial truss structure with rotational spring. Considering the geometric nonlinearity of the material, a bar element based on Ogden hyperelastic constitutive model is used to simulate the creases and virtual creases of the non-rigid origami structure, which can deal with the non-rigid origami structure with large overall motions and large deformations. A nonlinear rotational spring is introduced to reflect the bending resistance of the crease. Compared with the traditional rotational spring constitutive model, the modified nonlinear rotational spring constitutive model proposed in this paper has stronger versatility and robustness, and can effectively avoid the mutual penetration between the folding surfaces in contact-impact dynamics. Based on the principle of virtual work, the dynamic equations of the non-rigid origami multibody system considering the damping effect are established, which are solved by the variable-step generalized-α method. Finally, a series of numerical examples of three classical origami structures are presented to verify the accuracy and efficiency of the bar-and-hinge dynamics model proposed in this paper. Furthermore, by adding virtual creases and correcting the initial configuration, the locking problem of the unfolding and folding process in the rigid origami model is effectively resolved. Compared with the rigid origami model, the bar-and-hinge dynamics model can continue to perform further calculation and provide the fully deployed configuration with large deformation. On this basis, the complex dynamic behaviors of the non-rigid origami structure are revealed, and the mechanics characteristics of multi-stable, transient dynamics and wave dynamics are analyzed.