The high cost and relative scarcity of platinum (Pt) restrict large-scale commercialization of fuel cells, which has spurred researchers to develop low-cost alternatives integrating with high hydrogen evolution reaction (HER) and oxygen reduction reaction (ORR) catalytic activity. Herein, we performed density functional theory (DFT) calculations to explore the electrocatalytic activity of graphyne nanotubes (GyNTs). Several GyNTs were found to be potential metal-free electrocatalysts, with both HER and ORR activity superior to Pt. Moreover, we revealed a linear relationship between the Gibbs free energy change of O2 adsorption (ΔGOOH) and binding energy of H adsorption (ΔEH), which could be attributed to the fact that both the CO bond of OOH adsorption and the CH bond of H adsorption are single bonds. Therefore, ΔEH is proposed as a general descriptor for the rational design of bifunctional graphyne materials toward HERs and ORRs. Our findings provide a simple strategy for the rational design of bifunctional materials.