This study aimed to investigate structural and functional alterations of the reward system and the neurobiology of craving in alcohol use disorder (AUD). We hypothesized reduced volume of the nucleus accumbens (NAcc), reduced structural connectivity of the segment of the supero-lateral medial forebrain bundle connecting the orbitofrontal cortex (OFC) with the NAcc (OFC-NAcc), and reduced resting-state OFC-NAcc functional connectivity (FC). Furthermore, we hypothesized that craving is related to an increase of OFC-NAcc FC. Thirty-nine recently abstinent patients with AUD and 18 healthy controls (HC) underwent structural (T1w-MP2RAGE, diffusion-weighted imaging (DWI)) and functional (resting-state fMRI) MRI-scans. Gray matter volume of the NAcc, white matter microstructure (fractional anisotropy (FA)) and macrostructure (tract length) of the OFC-NAcc connection and OFC-NAcc FC were compared between AUD and HC using a mixed model MANCOVA controlling for age and gender. Craving was assessed using the thoughts subscale of the obsessive-compulsive drinking scale (OCDS) scale and was correlated with OFC-NAcc FC. There was a significant main effect of group. Results were driven by a volume reduction of bilateral NAcc, reduced FA in the left hemisphere, and reduced tract length of bilateral OFC-NAcc connections in AUD patients. OFC-NAcc FC did not differ between groups. Craving was associated with increased bilateral OFC-NAcc FC. In conclusion, reduced volume of the NAcc and reduced FA and tract length of the OFC-NAcc network suggest structural alterations of the reward network in AUD. Increased OFC-NAcc FC is associated with craving in AUD, and may contribute to situational alcohol-seeking behavior in AUD.