The study evaluates the efficacy of 1 week of tDCS (5 sessions) placebo in reducing alcohol consumption within the 24 weeks following the treatment in non-abstinent patients with alcohol use disorders versus placebo.

340 patients are expected and randomized in two groups: 170 patients with active tDCS and 170 patients with placebo tDCS

Visit 1 : Patients will received one daily session (13:20:13) during 5 consecutive days: current flows continuously twice for 13min with a rest interval (no stimulation) of 20 min.

Visit 1 to 7 : Change from baseline to week 24 in Total Alcohol Consumption (TAC) and Number of Heavy Drinking Days (HDD) will be evaluated in each group.

Evaluation on alcohol consumption (daily drinking diary, alcohol craving and severity) and other assessments like mood, quality of life, safety.

The co-primary outcome of change from baseline in total alcohol consumption AND reduction in number of heavy drinking days at 6 months after treatment and its association with tDCS will be analyzed under the intention-to-treat principle using a mixed model repeated measures (8 times).

Inclusion Criteria:

• Patients must have signed and dated the informed consent form
• Male and female patients over 18 years of age
• Patients who meet at least two criteria for Alcohol Use Disorder as defined in the Diagnostic and statistical Manual of mental disorder (DSM-5)
• Patients who are motivated to reduce their alcohol consumption
• At least one attempt to achieve abstinence (unsuccessful or relapse) or to reduce alcohol consumption

Exclusion Criteria:

• Breath-alcohol concentration > 0 milligrams per litre of exhaled air at randomization (visit 1)
• < 6 heavy drinking days in the 4 weeks before randomization (European Medicines Agency, 2010; a day with alcohol consumption ≥ 60 g for men and ≥40 g for women)
• An average alcohol consumption below medium risk level according to World health Organization (WHO) in the 4 weeks before screening (WHO, 2000; ≤40g/day for men; ≤20g/day for women),
• More than 3-days abstinence prior to screening and randomization (screening visit and visit 1)
• A Revised Clinical Institute Withdrawal Assessment for Alcohol score ≥ 10 (indicating the need for medication supported detoxification) at randomization (visit 1)
• Concomitant treatment with disulfiram, acamprosate, topiramate, baclofen, naltrexone, and nalmefene (<1 month)
• History of pre-delirium tremens and delirium tremens
• DSM-5 substance use disorder other than alcohol or nicotine use disorder
• Acute psychiatric disorders that have required hospitalisation and/or immediate adjustment of psychotropic medications
• Major depression, as defined by Hamilton Depression (HDRS) scale greater than or equal to 24
• Recent change in psychotropic medication (< 1 month)
• Severe chronic psychiatric disorders including schizophrenia, paranoia and bipolar disorder type I and II
• Advanced liver, kidney, cardiac, or pulmonary disease or other acute serious or unstable medical condition that would compromise patient's participation in the study according to physician's judgment
• Contra-indications to tDCS: metal in the head, implanted brain medical devices
• Women who are pregnant or lactating
• Women of childbearing potential with a positive urine β-human chorionic gonadotrophin pregnancy test at randomization (visit 1)
• Concurrent participation in other trial
• Employees of the investigator or trial site
• Patients protected by law
• Persons who are not covered by national health insurance
• Patients, in the opinion of the investigation, not able to complete the TLFB and to complete their daily alcohol consumption in a diary (derived from the TLFB) during the 3 months of the study.
• Patients who refused to sign "safety" agreement