Previous research has shown that stimulation of the left dorsolateral prefrontal cortex (DLPFC) enhances working memory (e.g. in the n-back task), and reduces craving for cigarettes and alcohol. Stimulation of the right inferior frontal gyrus (IFG) improves response inhibition. The underlying mechanisms are not clearly understood, nor is it known whether IFG stimulation also reduces craving. Here, we compared effects of DLPFC, IFG, and sham stimulation on craving in heavy drinkers in a small sample (n = 41). We also tested effects of tDCS on overcoming response biases due to associations between alcohol and valence and alcohol and approach, using implicit association tests (IATs). Mild craving was reduced after DLPFC stimulation. Categorization of valence attribute words in the IAT was faster after DLPFC stimulation. We conclude that DLPFC stimulation can reduce craving in heavy drinkers, but found no evidence for tDCS induced changes in alcohol biases, although low power necessitates caution.