This study was aimed at exploring the electroencephalographic features associated with alcohol use disorders (AUD) during a resting-state condition, by using quantitative EEG and Functional Connectivity analyses. In addition, we explored whether EEG functional connectivity is associated with trait impulsivity. Absolute and relative powers and Synchronization Likelihood (SL) as a measure of functional connectivity were analyzed in 15 AUD women and fifteen controls matched in age, gender and education. Correlation analysis between self-report impulsivity as measured by the Barratt impulsiveness Scale (BIS-11) and SL values of AUD patients were performed. Our results showed increased absolute and relative beta power in AUD patients compared to matched controls, and reduced functional connectivity in AUD patients predominantly in the beta and alpha bands. Impaired connectivity was distributed at fronto-central and occipito-parietal regions in the alpha band, and over the entire scalp in the beta band. We also found that impaired functional connectivity particularly in alpha band at fronto-central areas was negative correlated with non-planning dimension of impulsivity. These findings suggest that functional brain abnormalities are present in AUD patients and a disruption of resting-state EEG functional connectivity is associated with psychopathological traits of addictive behavior.