In this contribution, the design of a graphene-supported high-entropy single-atom catalyst (HESAC) composed of Fe, Co, Ni, and Ru metal atoms (FeCoNiRu-HESAC) is proposed. Negative formation energy and positive dissociation potentials indicate such materials' thermodynamic and electrochemical stability. Based on density functional theory (DFT) calculations, Co active sites lead to the overpotentials of 0.28 VRHE for oxygen evolution reaction (OER), 0.16 VRHE for hydrogen evolution reaction (HER), and 0.25 VRHE for CO2 reduction reaction (CO2RR) towards CO formation. These surpass the activity of CoN4 single-atom catalyst. More interestingly, the low CO2RR and HER overpotentials enable the FeCoNiRu-HESAC to produce syngas (CO + H2). In addition, the Fe, Ni, and Ru sites simply serve as counterparts to modify the performance of Co active sites through non-bonding interactions. Besides, machine learning (ML) implies that, the valence electrons of intermediates as well as the d orbital electrons of metal sites are the most important parameters affecting the reaction intermediates’ Gibbs free energy. According to these DFT and ML results, a strategy to design multifunctional HESACs electrocatalysts is developed.