Shape memory polymers (SMPs) are a class of smart materials which can recover from a deformed shape to their original shape by a certain external stimulus. To predict the deformation behaviors of SMPs, different constitutive models have been developed in the last few years. However, most of the constitutive models need many parameters to be determined by specific experiments and complex calibration processes. This drawback has limited their application in promoting the development of SMPs. Thus, it is imperative to develop a new constitutive model which is not only accurate, but also relatively simple. In our work, a novel fractional viscoelastic constitutive model coupling with time-temperature superposition principle is first proposed for SMPs. Then, frequency sweep and temperature sweep experiments are conducted to determine the parameters of the model. Finally, the shape memory free recovery experiments are carried out to validate the predictive capability of the developed model. By comparing the predicted results with experimental data, we find that though our model has only eleven parameters in total, it could capture the thermomechanical behaviors of SMPs in very good agreement with experimental results. We hope the proposed new model provide researchers with guidelines in designing and optimizing of SMP applications. (C) 2018 Wiley Periodicals, Inc.