The jointed rock mass exhibits an obviously instantaneous plastic strain under fatigue loading, and thus it is imperative to establish a fatigue constitutive model of jointed rock considering instantaneous plasticity. Based on the assumption that the relationship between the plastic stress of the joint and stress follows a power function, and the accelerated fatigue strain is a second-order nonlinear viscous strain, a joint plastic fatigue component and a double-triggered nonlinear viscous fatigue composite component are proposed. Then a new elastic-plastic viscous fatigue model of jointed rock is established. The results reveal that the proposed model can accurately simulate the fatigue strain of intact rock and jointed rock. Moreover, the proposed model can simulate the stationary fatigue curve of jointed rock mass under fatigue loading, and it can also be applied in the simulation of instantaneous elastic-plastic fatigue, decelerated fatigue, constant speed fatigue and accelerated fatigue of jointed rock under non-stationary fatigue. The model fitting results show that the instantaneous fatigue plastic strain of jointed rock accounts for a large proportion of the instantaneous fatigue strain which should not be ignored. The results of this study are of great reference value in the prediction of fatigue strain and fatigue stability of jointed rock in rock engineering.