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A thermoviscoelastic modeling approach is developed to predict the recovery behaviors of the thermally activated amorphous shape memory polymers (SMPs) based on the generalized finite deformation viscoelasticity theory. In this paper,a series of moduli and relaxation times of the generalized Maxwell model is estimated from the stress relaxation master curve by using the nonlinear regression(NLREG)method. Assuming that the amorphous SMPs are approximately incompressible isotropic elastomers in the rubbery state,the hyperelastic response of the materials is well modeled with a hyperelastic model in Ogden form. In addition,the Williams-Landel-Ferry(WLF) equation is used to describe the horizontal shift factor obtained with time-temperature superposition principle (TTSP). The finite element simulations show good agreement with the experimental thermomechanical behaviors. Moreover,the possibility of developing a temperature-responsive intravascular stent with the SMP studied here is investigated in terms of its thermomechanical property. Therefore,it can be concluded that the model has good prediction capabilities for the recovery behaviors of amorphous SMPs.