Active threat avoidance is an adaptive coping strategy but can evolve into maladaptive behavior patterns when it is disproportionate to an actual threat. While excessive and persistent avoidance, as often seen in anxiety-related disorders, have been investigated extensively, it is presently unclear under what circumstances insufficient avoidance might occur in the presence of a genuine threat. We hypothesized that anhedonia, the reduced ability to experience pleasure, might undermine the relief experience after successful threat avoidance and thus reduce future active avoidance responses. Using an established avoidance learning paradigm, we examined the relationship between anhedonia, relief, and active avoidance responses. Forty participants learned that two threat cues signaled electrical stimulation and they could click a button during cue presentations to prevent electrical stimulation from occurring. While clicking the button worked for one threat cue, it did not work for the other one. After several repetitions, button effectiveness was reversed. Another safety cue that never signaled electrical stimulation was presented intermixed with the two threat cues. Every time there was an omission of electrical stimulation, self-reported relief was measured. We found that participants who scored higher on anhedonia experienced weaker relief during all outcome omissions. Behaviorally, at the early stage of each phase, participants who scored higher on anhedonia executed fewer avoidance actions, specifically for the threat cue that signaled avoidable electrical stimulation. Relief induced by threat omission is a pleasant experience, which trait anhedonia seems to impair. This attenuation of relief might reduce the reinforcement of future adaptive avoidance behaviors.