In this work, to describe the cycle behavior considering fatigue-creep interaction, a non-unified viscoplastic constitutive model for 316 stainless steel is derived within the irreversible thermodynamic framework. The internal variables considering kinematic and isotropic hardening properties are selected to construct the evolution equation of visco-plastic and creep terms. The proposed constitutive model was validated by the comparison with the existing literature. It was manifested that this constitutive model could successfully predict the hardening behavior and stress relaxation process under the cyclic loading. During the dwell period, the increment of the inelastic strain is decomposed into the viscoplastic and creep term. The viscoplastic deformation dominates first stage of the stress relaxation, while the stable stage is controlled by the creep term. Finally, the predicted values of mean stress are taken into the Manson-Coffin law, the low cycle fatigue life prediction are carried out based on the numerical model, which showed robust correlation with experimental results.