Strain controlled fatigue of P92 steel with various strain hold dwells introduced at the peak loading point were conducted at 625 °C. Two features which depend on the cycle and strain range level were observed under the fatigue-creep condition for the viscous and cyclic softening material. The first one is the accelerated cyclic softening response which is ascribed to the accumulated inelastic strain transformation from the creep mechanism during the strain dwell period and becomes more significant with the decrease of strain ranges. The second one is the decelerated stress relaxation behavior which is caused by the reduced viscous stress related to the continuous cyclic softening and fades with the decrease of cyclic strain ranges. Accordingly, a new unified viscoplastic constitutive model within the framework of Chaboche model was developed by improving the nonlinear isotropic hardening rule and the kinematic hardening rule with a cyclic softening parameter. As a result, the accelerated cyclic softening and decelerated stress relaxation response of fatigue-creep interaction was finely reproduced by the proposed model. •Strain controlled fatigue of P92 with various strain hold dwells introduced at the peak loading point were conducted at 625 °C.•The accelerated cyclic softening response increases with the decrease of strain ranges due to the strain dwell.•The decelerated stress relaxation behavior fades with the decrease of cyclic strain ranges due to the continuous cyclic softening.•A unified viscoplastic constitutive model was developed by improving the kinematic hardening rule with a cyclic softening parameter.