In this paper, the origami membrane is modeled as a flexible multibody system and its deployment is simulated based on the absolute nodal coordinate formulation. The nonlinear anti-deployment effect of crease is integrated into the multibody system via the virtual work principle. The facet is modeled by the thin shell element and the crease is constructed as a nonlinear torsional spring with specific position and gradient constraints. The behavior of the crease is parameterized based on the experimental data. The modeling approach is verified by the numerical/experimental reference of the Z-folding structure in the existing literature. For the multi-crease origami membrane model considering the crease effect, a form-finding method to obtain the initial configuration of the flexible origami is proposed based on the principle of minimum potential energy. The deployment of the classical Miura-ori unit membrane structure is analyzed. The magnitude of driving force is estimated based on the force analysis of rigid deployment. Based on the simulation result of flexible deployment, the driving force is planned to achieve a stable deployment with a constant increase speed in the deployment ratio. This work is expected to provide a reference for the design of space membrane structure, the estimation of driving force, and optimizing the deployment strategy of an origami membrane.