Alcohol use disorder (AUD) is characterized by enhanced cue-reactivity and the opposing control processes being insufficient. The ability to inhibit reactions to alcohol-related cues, alcohol-specific inhibition, is thus crucial to AUD; and trainings strengthening this ability might increase treatment outcome. The present study investigated whether neurophysiological correlates of alcohol-specific inhibition (I) vary with craving, (II) predict drinking outcome in AUD and (III) are modulated by alcohol-specific inhibition training. A total of 45 recently abstinent patients with AUD and 25 controls participated in this study. All participants underwent functional magnetic resonance imaging (fMRI) during a Go-NoGo task with alcohol-related as well as neutral conditions. Patients with AUD additionally participated in a double-blind RCT, where they were randomized to either an alcohol-specific inhibition training or an active control condition (non-specific inhibition training). After the training, patients participated in a second fMRI measurement where the Go-NoGo task was repeated. Percentage of days abstinent was assessed as drinking outcome 3 months after discharge from residential treatment. Whole brain analyses indicated that in the right inferior frontal gyrus (rIFG), activation related to alcohol-specific inhibition varied with craving and predicted drinking outcome at 3-months follow-up. This neurophysiological correlate of alcohol-specific inhibition was however not modulated by the training version. Our results suggest that enhanced rIFG activation during alcohol-specific (compared to neutral) inhibition (I) is needed to inhibit responses when craving is high and (II) fosters sustained abstinence in patients with AUD. As alcohol-specific rIFG activation was not affected by the training, future research might investigate whether potential training effects on neurophysiology are better detectable with other methodological approaches.