Non-precious metal and nitrogen codoped carbon catalysts have emerged as promising candidates to replace noble platinum (Pt)-based catalysts in the processes of the oxygen reduction reaction (ORR) and the hydrogen evolution reaction (HER). Herein, we use a 1D/2D hybrid strategy to synthesize a Co,N-codoped carbon nanotube (CNT)/graphene heterostructure bifunctional catalyst (Co/NCNT/NG). The Co/NCNT/NG heterostructure catalyst shows not only a positive half-wave potential of 0.85 V ( versus RHE) and long-term stability for the ORR, but also a low overpotential of 123 mV at a current density of 10 mA cm −2 and ultrahigh stability in 0.5 M H 2 SO 4 for the HER. The superior performance of the Co/NCNT/NG catalyst is attributed to the inimitable 1D/2D CNT/graphene heterostructure, in which 1D and 2D structures provide different catalytically active sites (including metallic Co, CoN 2 and N–C) for the HER and ORR, respectively. Moreover, the catalyst also exhibits similar discharge performance and robust durability as an air electrode in Zn–air batteries to the Pt-based one. This work provides a new approach for the in situ synthesis of bifunctional and multifunctional catalysts by integrating 1D/2D/3D materials with different catalytically active sites into one heterostructure.