The neural bases of cognitive impairment(s) in alcohol use disorders (AUDs) might reflect either a global brain damage underlying different neuro-cognitive alterations, or the involvement of specific regions mostly affected by alcohol neuro-toxic effects. While voxel-based-morphometry (VBM) studies have shown a distributed atrophic pattern in fronto-limbic and cerebellar structures, the lack of comprehensive neuro-cognitive assessments prevents previous studies from drawing robust inferences on the specificity of the association between neuro-structural and cognitive impairments in AUDs. To fill this gap, we addressed the neuro-structural bases of cognitive impairment in AUDs, by coupling VBM with an in-depth neuropsychological assessment. VBM results highlighted a diffuse pattern of grey matter reduction in patients, involving the key-nodes of the meso-cortico-limbic (striatum, hippocampus, medial prefrontal cortex), salience (insular and dorsal anterior cingulate cortex) and executive (inferior frontal cortex) networks. Grey matter density in the insular and anterior cingulate sectors of the salience network, significantly decreased in patients, explained almost half of variability in their defective attentional and working-memory performance. The multiple cognitive and neurological impairments observed in AUDs might thus reflect a specific executive deficit associated with the selective damage of a salience-based neural mechanism enhancing access to cognitive resources required for controlled cognition and behaviour.