In authors’ previous work (Chen et al. in Appl Phys A. doi: 10.1007/s00339-016-0371-6 , 2016), the nonlinear unloading behavior of a typical Ni-based superalloy was investigated by hot compressive experiments with intermediate unloading–reloading cycles. The characters of unloading curves were discussed in detail, and a new elasto-viscoplastic constitutive model was proposed to describe the nonlinear unloading behavior of the studied Ni-based superalloy. Still, the functional relationships between the deformation temperature, strain rate, pre-strain and the parameters of the proposed constitutive model need to be established. In this study, the effects of deformation temperature, strain rate and pre-strain on the parameters of the new constitutive model proposed in authors’ previous work (Chen et al. 2016) are analyzed, and a unified elasto-viscoplastic constitutive model is proposed to predict the unloading behavior at arbitrary deformation temperature, strain rate and pre-strain.