Tuning metal-support interaction has been considered as an effective approach to modulate the electronic structure and catalytic activity of supported metal catalysts. At the atomic level, the understanding of the structure-activity relationship still remains obscure in heterogeneous catalysis, such as the conversion of water (alkaline) or hydronium ions (acid) to hydrogen (hydrogen evolution reaction, HER). Here, we reveal that the fine control over the oxidation states of single-atom Pt catalysts through electronic metal-support interaction significantly modulates the catalytic activities in either acidic or alkaline HER. Combined with detailed spectroscopic and electrochemical characterizations, the structure-activity relationship is established by correlating the acidic/alkaline HER activity with the average oxidation state of single-atom Pt and the Pt-H/Pt-OH interaction. This study sheds light on the atomic-level mechanistic understanding of acidic and alkaline HER, and further provides guidelines for the rational design of high-performance single-atom catalysts.