Binge eating disorder (BED) is a common mental disorder, closely associated with obesity. Existing treatments are only moderately effective with high relapse rates, necessitating novel interventions. This paper describes the rationale for, and protocol of, a feasibility randomised controlled trial (RCT), evaluating the combination of transcranial direct current stimulation (tDCS) and a computerised cognitive training, namely approach bias modification training (ABM), in patients with BED who are overweight or obese. The aim of this trial is to obtain information that will guide decision-making and protocol development in relation to a future large-scale RCT of combined tDCS+ABM treatment in this group of patients, and also to assess the preliminary efficacy of this intervention.