Based on the DFT calculations, two-dimensional (2D) R-graphyne has been demonstrated to have high stability and good conductivity, which can be conducive to the relevant electrocatalytic activity of the material. Different from the poor graphene, R-graphyne, which is completely composed of anti-aromatic structural units, can exhibit certain HER catalytic activity. In addition, doping the TM atoms in Group VIIIB can be considered an effective strategy to enhance the HER catalytic activity of R-graphyne. Particularly, Fe@R-graphyne, Os@R-graphyne, Rh@R-graphyne and Ir@R-graphyne can exhibit higher HER catalytic activities due to the formation of more active sites. Usually, the shorter the distance between the TM and C atoms is, the better the HER activity of the C-site is. Furthermore, doping Ni and Rh atoms of Group VIIIB can significantly improve the OER catalytic performance of R-graphyne. It can be found that ΔGO*can be used as a good descriptor for the OER activities of TM@R-graphyne systems. Both Rh@R-graphyne and Ni@R-graphyne systems can exhibit bifunctional electrocatalytic activities for HER/OER. In addition, all the relevant catalytic mechanisms are analyzed in detail. This work not only provides nonprecious and highly efficient HER/OER electrocatalysts, but also provides new ideas for the design of carbon-based electrocatalysts.