Shape memory polymers (SMPs) are one of the polymeric smart materials which can undergo transition between two different shapes (temporary shape and permanent shape) induced by external stimuli, such as temperature, light etc. Increasing applications of SMPs have motivated a great progress in developing adequate constitutive models for this kind of material. In this work, we propose a new constitutive model of SMPs combining phase transition and viscoelasticity. The SMP materials are treated as a mixture of rubbery phase and glassy phase. Thus, it can physically relate the shape memory effect to glass transition. As the proposed model is also based on viscoelastic theory, it can successfully characterize the viscoelastic properties and predict the rate-dependent shape memory response of SMPs. By ignoring the viscosity of the material, the proposed model could be degenerated to a purely elastic phase transition model. To verify the model, we have simulated the shape memory behavior of polyurethane under different pre-strains and have compared the simulation results with the experimental results available in the literature. Good agreement between numerical calculations and experiments can be observed. (C) 2018 Elsevier Ltd. All rights reserved.