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[Display omitted] • The bifunctional catalytic mechanism of LaN x C 4-x -Gra for ORR and OER in acidic and alkaline environments was discussed for the first time. • OH modification is helpful to the improvement of catalytic activity for ORR, but adverse for OER. • LaN 2 C 2 hex-Gra exhibits potential bifunctional activity in alkaline environment and also shows excellent OER activity in acidic environment. • The descriptor f-band center was introduced to rapidly predict catalytic activity. The oxygen reduction/evolution reaction (ORR/OER) on oxygen electrode are the definitive reactions in charge/discharge process of fuel cells and metal air batteries. The research of bifunctional and acidic-alkaline omnipotent electrocatalysts for the oxygen electrode reaction is of great significance for the development and application of electrochemical storage and conversion technologies. In this paper, the catalytic performance of the rare earth LaN x C 4-x -doped graphene (LaN x C 4-x -Gra) catalysts has been discussed extensively. The results demonstrate that in the alkaline environment, LaN 2 C 2 hex-Gra exhibits potential bifunctional activity with the original ηOER is 0.68 V, and the ηORR is 0.56 V accompanied by OH ligands modified. Impressive, LaN 2 C 2 hex-Gra also shows excellent OER activity in acidic environment with the η of 0.68 V. Finally, the catalytic activity can be rapidly evaluated by scale relationship with the introduced band center, which will provide guidance for the development of efficient rare earth single atomic catalysts. [ABSTRACT FROM AUTHOR]