The evolution of bifunctional catalysts for the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) catalysts that are highly active, stable, and conductive is crucial for advancing metal-air batteries and fuel cells. We have here thoroughly explored the OER and ORR performance for a category of two-dimensional (2D) metal-organic frameworks (MOFs) called TM3(HADQ)2, and Rh3(HADQ)2 exhibits a promising bifunctional OER/ORR activity, with an overpotential of 0.31 V for both OER and ORR. The d-band center (εd) and crystal orbital Hamilton populations (COHP) are utilized to study the relationship between OER/ORR activity and the electronic structure of catalysts, and it is found that the elementary d-electron number (Ne) of the central TM for TM3(HADQ)2, as well as the electronegativity of the ligand TM-N4 and the intermediate O atom, are the main reason that affects the catalytic activity of OER/ORR. Additionally, Rh3(HADQ)2 can be proven through the constant potential method (CPM) and microkinetics method that it is an acidic OER/ORR bifunctional catalyst. Rh3(HADQ)2 has a high toxicity tolerance, making it a potential bifunctional catalyst. Our research contributes to both the rational design of SACs for various catalytic processes and the fabrication of bifunctional, cost-effective oxygen-electric catalysts.