In order to deeply explore the high-temperature cyclic characteristics of the FGH96 superalloy under different strain amplitudes, the high-temperature low-cycle fatigue behavior of the FGH96 superalloy was analyzed from the perspective of internal stress evolution. Four sets of strain amplitude (0.5%, 0.6%, 0.8%, and 1.2%) controlled high-temperature low-cycle fatigue tests were carried out on the FGH96 superalloy at 550 °C, and the internal stress was divided into back stress and effective stress through the cyclic stress-strain curves. The results show that the cyclic softening/hardening characteristics of the FGH96 superalloy under different strain amplitudes are closely related to the evolution of internal stress. The strain amplitude has a significant effect on the back stress of the FGH96 superalloy but has little effect on effective stress. At low strain amplitudes (0.5% and 0.6%), the back stress evolution rate of the FGH96 superalloy is lower than effective stress, and the material mainly exhibits cyclic softening. At high strain amplitudes (0.8% and 1.2%), the back stress evolution rate of the FGH96 superalloy is significantly higher than effective stress, and the material exhibits cyclic hardening. The combined effect of back stress and effective stress is the main reason for the different low-cycle fatigue behaviors of the FGH96 superalloy under different strain amplitudes.