Shape memory polymer composite (SMPC) hinges have been researched as deployable structures in space missions due to their stable and controllable shape recovery behaviors. The elastic energy of the fabrics plays a dominant role in predicting the recovered shape of the hinges, as it strongly drives shape restoration. In this research, the shape recovery behaviors of SMPC hinges are numerically investigated by applying an equation that accounts for the hysteresis characteristics of the fabric reinforcement. The constitutive equation integrates the Mooney–Rivlin model, a viscoelastic, stored energy model, to characterize the hyperelastic properties varying with time, temperature, and shape recovery behaviors of the SMP matrix. Additionally, polynomial functions are introduced to represent the hysteresis effects and energy dissipation behavior of the fabrics. Since the elasticity of fabrics significantly affects the shape recovery of SMPCs, the developed constitutive equation enables accurate prediction of the recovered configuration. Finite element method analysis is performed based on this model and validated through comparison with experimental results. Finally, the constitutive equation is applied to investigate the shape memory response of SMPC hinges. The simulations present the significant design factors to increase the shape recovery ratio of the SMPC hinges.