Origami structures gradually emerge at the frontier of engineering applications because of their characteristics of reconfigurable shape, tunable stiffness, and excellent energy absorption. Although a wealth of algorithms and software are available for origami design and folding analysis, they are generally isolated from other computational tools. Therefore, this study proposes an integrated parametric origami design workflow, based on Grasshopper combined with multi-objective optimization. First, a parametric model for ring-shaped four-fold origami structure is developed based on geometric parameters. Its nonlinear folding process is then simulated according to geometric compatibility conditions and given constraints. Simultaneously, modal analysis is iteratively performed by calling SAP2000 through C# scripts, to obtain the quantitative relationships between the configuration, mass, and stiffness. Finally, an inverse design of the cylindrical annulus is carried out using Octopus, considering the spatial fit aspect, the structural stiffness, and the structural mass. Comparison with the results of the Origami Simulator and the physical models validates that the proposed method accurately simulates the actual motion of the ring-shaped four-fold origami structure. The parametric analysis demonstrates that during the change of partial geometric parameters, the mass of the structure decreases but the stiffness increases. After balancing the three indicators in inverse design, a recommended range of parameters is given for the circular origami structures limited to spatial size. Notably, the workflow ensures a direct link between geometry, kinematics, and structural performance, and has access to customizing origami structures with desirable geometry and mechanical properties.