Alcohol addiction is accompanied by aberrant neural activity. Previously, task-based fMRI and resting-state EEG studies have revealed that craving, a critical component of addiction, is linked to abnormal activity in cortical regions including the dorsal anterior cingulate cortex (dACC), nucleus accumbens (NAcc), posterior cingulate cortex (PCC) and pregenual anterior cingulate cortex (pgACC), etc. In this study, we combine these two imaging techniques to investigate a group of alcohol-addicted patients and provide convergent evidence for the neural correlates of craving not only in alcohol but substance abuse in general. We observe abnormal BOLD signal levels in the dACC, NAcc, pgACC, PCC, amygdala, and parahippocampus (PHC) in a cue-reactivity fMRI experiment. These findings are consistent with increased beta-band activity in the dACC and pgACC in resting-state EEG. We further observe desynchronization characterized by decreased functional connectivity in cue-based fMRI and hypersynchronization characterized by increased functional connectivity between these regions in the theta frequency band. The results of our study show a consistent pattern of alcohol craving elicited by external cues and internal desires. Given the advantage of superior spatial and temporal resolution, we hypothesize a "central craving network" that integrates the different aspects of alcohol addiction into a unified percept.