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Background The left dorsolateral prefrontal cortex (DLPFC) is involved in early-phase manual dexterity skill acquisition when cognitive control processes, such as integration and complexity demands, are required. However, the effectiveness of left DLPFC transcranial direct current stimulation (tDCS) on early-phase motor learning and whether its effectiveness depends on the cognitive demand of the target task are unclear. This study aimed to investigate whether tDCS over the left DLPFC improves non-dominant hand dexterity performance and determine if its efficacy depends on the cognitive demand of the target task. Methods In this randomized, double-blind, sham-controlled trial, 70 healthy, right-handed, young adult participants were recruited. They were randomly allocated to the active tDCS (2 mA for 20 min) or sham groups and repeatedly performed the Purdue Pegboard Test (PPT) left-handed peg task and left-handed assembly task three times: pre-tDCS, during tDCS, and post tDCS. Results The final sample comprised 66 healthy young adults (mean age, 22.73 ± 1.57 years). There were significant interactions between group and time in both PPT tasks, indicating significantly higher performance of those in the active tDCS group than those in the sham group post tDCS (p Conclusions These results demonstrated that prefrontal tDCS significantly improved early-phase manual dexterity skill acquisition, and its benefits were greater for the task with high cognitive demands. These findings contribute to a deeper understanding of the underlying neurophysiological mechanisms of the left DLPFC in the modulation of early-phase dexterity skill acquisition. Trial registration: This study was registered in the University Hospital Medical Information Network Clinical Trial Registry in Japan (UMIN000046868), Registered February 8, 2022 https://center6.umin.ac.jp/cgi-open-bin/ctr_e/ctr_view.cgi?recptno=R000053467