Transcranial direct current stimulation (tDCS) is an innovative technique recently shown to improve language outcomes even in neurodegenerative conditions such as primary progressive aphasia (PPA), but the underlying brain mechanisms are not known. The present study tested whether the additional language gains with repetitive tDCS (over sham) in PPA are caused by changes in functional connectivity between the stimulated area (the left inferior frontal gyrus (IFG)) and the rest of the language network. We scanned 24 PPA participants (11 female) before and after language intervention (written naming/spelling) with a resting-state fMRI sequence and compared changes before and after three weeks of tDCS or sham coupled with language therapy. We correlated changes in the language network as well as in the default mode network (DMN) with language therapy outcome measures (letter accuracy in written naming). Significant tDCS effects in functional connectivity were observed between the stimulated area and other language network areas and between the language network and the DMN. TDCS over the left IFG lowered the connectivity between the above pairs. Changes in functional connectivity correlated with improvement in language scores (letter accuracy as a proxy for written naming) evaluated before and after therapy. These results suggest that one mechanism for anodal tDCS over the left IFG in PPA is a decrease in functional connectivity (compared to sham) between the stimulated site and other posterior areas of the language network. These results are in line with similar decreases in connectivity observed after tDCS over the left IFG in aging and other neurodegenerative conditions.