A priori normative beliefs, the precondition of social norm compliance that reflects culture and values, are considered unique to human social behavior. Previous studies related to the ultimatum game revealed that right lateral prefrontal cortex (rLPFC) has no stimulation effects on normative beliefs. However, no research has focused on the effects of a priori belief on the rLPFC in voluntary cooperation attached to the public good (PG) game. In this study, we used a linear asymmetric PG to confirm the influence of the rLPFC on a priori normative beliefs without threats of external punishment through transcranial direct current stimulation (tDCS). Participants engaged via computer terminals in groups of four (i.e., two high-endowment players with 35G$ and two low-endowment players with 23G$). They were anonymous and had no communication during the entire process. They were randomly assigned to receive 15 min of either anodal, cathodal, or sham stimulation and then asked to answer questions concerning a priori normative beliefs (norm.belief and pg.belief). Results suggested that anodal/cathodal tDCS significantly (P < 0.001) shifted the participants’ a priori normative beliefs in opposite directions compared to the shift in the sham group. In addition, different identities exhibited varying degrees of change (28.80–54.43%). These outcomes provide neural evidence of the rLPFC mechanism’s effect on the normative beliefs in voluntary cooperation based on the PG framework.