In order to investigate the compressive mechanical properties of fiber-reinforced autoclaved aerated concrete (FAAC) under cyclic loading, a total of 11 sets of prismatic specimens were designed for uniaxial monotonic and cyclic compression tests. The effects of fiber types (basalt fiber, BF, carbon fiber, CF) and fiber content on the mechanical performance indicators of FAAC such as failure mode, stress-strain curve characteristics, plastic strain, stiffness degradation rate, and stress degradation rate, were analyzed. The research results indicate that the failure mode of FAAC under cyclic loading contains oblique shear failure and vertical splitting failure, and with the fiber content increasing, the failure mode of FAAC turns from shear failure to splitting failure. When the fiber content is 0.4%, the peak stresses of FAAC reach their maximum values, the peak stresses of BF/AAC under monotonic and cyclic loading increase 24.29% and 29.16%, respectively, while that of CF/AAC increase 31.45% and 37.81%, respectively. When the fiber content is 0.5%, the peak strains of FAAC reach their maximum values, the peak strains of BF/AAC under monotonic and cyclic loading increase 28.12% and 28.77%, respectively, while that of CF/AAC increase 37.17% and 41.50%, respectively. Both BF and CF slightly improve the cumulative plastic strain of AAC, but there is no significant relationship between fiber content, unloading stiffness, and stress degradation rate. Based on the experimental results, a power function is used to fit the relationship between the standardized plastic stain and unloading strain. Simplified double line models for stress degradation rate, unloading and reloading curves are proposed. Finally, the stress-strain curve calculation equation for FAAC under cyclic loading is established.