Display omitted •The catalytic bifunctional ORR/OER catalysts are firstly constructed.•The Co2P/CoP@NPGCs with active Co2P/CoP and Co-Nx sites adsorb ORR/OER-relevant reactants.•The N, P dual-doped carbon supports supply various active sites for ORR/OER.•The stable polyhedron core–shell MOFs precursor enhances the catalyst stability.•The Co2P/CoP@NPGCs shows higher ORR/OER activity than the Pt/C and RuO2. In this study, Co2P/CoP hybrid nanoparticles (NPs) imbedded on the surface of core–shell metal–organic frameworks (MOFs) derived three-dimensional N, P co-doped graphitized carbon (Co2P/CoP@NPGC) are prepared via direct pyrolysis of P-containing MOF precursors. P dopant dosage is tailored to adjust active sites and crystalline phases of Co2P/CoP@NPGC. The active Co2P and CoP NPs and the synergistic effect from the Co-Nx/C and Co-P/C active sites and porous NPGC make the dominant contributions to the ORR/OER. For ORR, the half-wave potential of Co2P/CoP@NPGC-1 is 0.93 V, which is superior to that of Pt/C (E1/2 = 0.875 V). As for OER, Co2P/CoP@NPGC-1 displays a lower overpotential (ƞ = 340 mV) compared to RuO2 (ƞ = 380 mV, at 10 mA cm−2). The Co2P@CoOOH heterojunction guarantees intrinsic conductivity. Furthermore, doping with N and P can modify the surface electronic structure of catalyst to lower the energy of oxygen adsorption and dissociation, which are beneficial to enhance the ORR and OER activity. Additionally, its bifunctional activity parameter (ΔE) for ORR and OER is only 0.64 V, which is lower than that of Pt/C and RuO2 (0.76 V). Therefore, this work proposes a new sight into constructing a competitive core–shell MOFs derived electrocatalyst for ORR/OER.