Oxygen evolution and reduction reactions (OER and ORR) are essential to the development of renewable energy conversion and storage technologies. For the first time, we investigate newly experimentally realized two-dimensional hexaaminobenzene-based coordination polymers (2D HAB-CPs) as OER and ORR catalysts through computational screening approach. We find that the interaction strength between intermediates and the transition metal complex (TM-N4) govern the catalytic activity of 2D HAB-CPs for OER and ORR. The interaction strength is strongly contingent on d-band centers, which can be modulated by changing TM atoms with different d-electron occupations. This modification of the interaction strength allows us to screen out the catalyst with the best catalytic performance. The best catalyst for OER is 2D Rh-HAB-CP with an over-potential ( η ) of 0.32V, followed by Co-HAB-CP (0.41V), while for ORR, Fe-HAB-CP has a smallest maximum free energy change ( Δ G max 1.23 ) of 0.52eV under equilibrium potential. Furthermore, these results inspire us to design a bifunctional OER/ORR catalyst by mixing Fe/Co precursors in 2D HAB-CP with the ORR/OER theoretical overpotentials even lower than that of the best ORR/OER catalysts (Pt/RuO2). In addition, all the 2D HAB-CPs are metallic due to the effects of d-p-π conjugation, which ensures fast electron transfer during the electrochemical reactions. Our findings highlight a new family of 2D materials as efficient non-precious-metal metal-air battery catalyst and offer a novel strategy in catalyst design.