Recently, the dynamic properties of brain activity rather than its stationary values have attracted more interest in clinical applications. It has been shown that brain signals exhibit scale-free dynamics or long-range temporal correlations (LRTC) that differ between rest and cognitive tasks in healthy controls and clinical groups. Little is known about how fear-inducing tasks may influence dispersion and the LRTC of subsequent resting-state brain activity. In this study, we aimed to explore the changes in the variance and scale-free properties of the brain's blood oxygenation level-dependent (BOLD) signal during the resting-state sessions before and after fear learning and fear memory extinction. During a 1-h break between magnetic resonance imaging (MRI) scanning, 23 healthy, right-handed volunteers experienced a fear extinction procedure, followed by Pavlovian fear conditioning that included partial reinforcement using mild electrical stimulation. We extracted the average time course of the BOLD signal from 245 regions of interest (ROIs) taken from the resting-state functional atlas. The variance of the BOLD signal and the Hurst exponent (H), which reflects the scale-free dynamic, were compared in the resting states before and after fear learning and fear memory extinction. After fear extinction, six ROIs showed a difference in H at the uncorrected level of significance, including areas associated with fear processing. H decreased during fear extinction but then became higher than before fear learning, specifically in areas related to the fear extinction network (FEN). However, activity in the other ROIs restored the H to its initial level. The variance of the BOLD signal in six ROIs demonstrated a significant increase from initial rest to the post-task rest. A limited number of ROIs showed changes in both H and variance. Our results imply that the variability and scale-free properties of the BOLD signal might serve as additional indicators of changes in spontaneous brain activity related to recent experience.