Apraxia of speech is a persistent speech motor disorder that affects speech intelligibility. Studies on speech motor disorders with transcranial Direct Current Stimulation (tDCS) have been mostly directed to post-stroke aphasia. Only a few tDCS studies have focused on apraxia of speech or childhood apraxia of speech (CAS), and no study has investigated individuals with CAS and people with trisomy 21 (T21, Down Syndrome). This study examined the effects of tDCS combined with a motor learning task in developmental apraxia of speech co-existing with T21 (ReBEC RBR-5435x9). The accuracy of speech sound production of nonsense words (NSWs) during Rapid Syllable Transition Training (ReST) under 10 sessions of anodal tDCS (1.5 mA, 25 cm) over the Broca’s area with cathode over the contralateral region was compared to 10 sessions of sham-tDCS and 4 control sessions in a 20-year-old male individual with T21 presenting moderate-severe childhood apraxia of speech (CAS). The accuracy for NSWs production progressively improved (gain 40%) under tDCS only (sham-tDCS and control sessions showed <20% gain). A decrease in speech severity from moderate-severe to mild-moderate indicated transfer effects in speech production. The speech accuracy under tDCS was correlated with Wernicke’s area activation (P3 current source density), which in turn, was correlated with the activation of the left supramarginal gyrus and the Sylvian Parietal Temporal Junction. Repetitive bihemispheric tDCS paired with ReST may have facilitated the speech sound acquisition in a young adult with T21 and CAS, possibly by recruiting brain regions required for the phonological working memory.