Here, we study a low-power technique for displays based on gaze tracking, called peripheral dimming. In this work, the threshold levels of the lightness reduction ratio (LRR), where people notice differences in brightness, depending on gaze positions and image brightness, are investigated. A psychophysical experiment with five gaze positions and three image brightness conditions is performed, and the estimated threshold levels are obtained. To investigate the significance of the differences between the threshold levels, the overlap method and the Bayesian estimation (BEST) analysis are performed. The analysis results show that the difference of the threshold levels depending on the conditions is insignificant. Thus, the proposed technique can operate with a constant LRR level, regardless of the gaze position or image brightness, while maintaining the perceptual image quality. In addition, the proposed technique reduces the power consumption of virtual reality (VR) displays by 12–14% on average. We believe that the peripheral dimming technique would contribute to reducing the power of the self-luminous displays used for VR headsets with an integrated eye tracker.