[Purposes] The paper aims to reveal the evolution law of fatigue damage of single fracture rock mass under cyclic loading, and to study the calculation method of damage variables that is more conducive to practical engineering application. [Methods] Through model rock fatigue tests based on acoustic wave velocity, the change law of wave velocity reduction rate, initial damage and damage variables under different cyclic times ratio and different single fracture angles were analyzed. A nonlinear fatigue cumulative damage model for different single fracture angles was proposed. [Findings] With the increase of the fracture angle, the decrease rate of the initial wave velocity and the initial damage of the model sample showed a nonlinear S-shaped trend. The wave velocity reduction rate of single fracture rock mass under cyclic load presented obvious three-stage attenuation characteristics, and the proportion of initial attenuation, stable attenuation and accelerated attenuation to fatigue life is about 2∶7∶1. At the same cycle number ratio, the fatigue cumulative damage evolution of rock mass tended to accelerate with the increase of fracture angle, but showed a decelerating trend in the accelerating attenuation stage. The relationship curve between fatigue life and fracture angle of single fracture rock mass is in "V" shape. Under cyclic loading, the damage variable of the rock mass with 45° fracture increased fastest, while the proportion of the fatigue life in the acceleration attenuation stage was the least, and the X-shaped fracture failure of the mixed tension compression shear fracture was most likely to occur. [Conclusions] If the nominal damage was substituted for the actual total damage before the fatigue failure of rock mass when the fracture was 30°~90°, the nominal damage value was larger. Once the nominal damage was replaced by the actual total damage in the fatigue failure stage, the nominal damage value was smaller. Meanwhile, a nonlinear fatigue cumulative damage model for rock masses with different single fracture angles was proposed. When the instability scale factor is constant, both the instability factor and the convergence factor show a monotonically increasing trend with the increase of the fracture angle.