To solve the slow dynamics of catalytic oxygen reaction energy devices, a facile method was developed for the synthesis of methylene alcohol terminated poly(1,4-phenyldiimine) porphyrin cobalt (M-PImPorCo), which was synthesized by RuCl₃ catalyzed redox reaction of meso-5,10,15,20-tetra(4-nitrophenyl) porphyrin cobalt (TNO₂PorCo) and 1,4-phenyldimethanol. M-PImPorCo is a fully conjugated covalent organic framework (COF) with high thermal and chemical stability. COFs with different edge groups were synthesized to compare the effect of different groups (–CH₂–OH and –NO₂) on catalytic bifunctional oxygen reaction activity. C=N as nitrogen-rich environment of M-PImPorCo leads to the protonation process of oxygen catalysis and reduces the energy barrier of adsorption in the oxygen intermediate. C=N and –CH₂–OH form an “electron pump” structure to deliver electrons to the Co–N₄ site in M-PImPorCo, and the π–π interaction between M-PImPorCo and three-dimensional graphene (3D-G) can further enrich the electron cloud density of Co–N₄ sites. M-PImPorCo/3D-G has remarkable oxygen catalytic performance, with a half-wave potential (E_1/2) of 0.91 V vs. reversible hydrogen electrode (RHE). M-PImPorCo/3D-G has low potential (E_j=10 is 1.49 V vs. RHE) at a current density of 10 mA·cm⁻². It exhibits a good bifunctional catalytic performance (potential difference (ΔE) = 0.58 V). The smaller charge–discharge band gap of zinc-air batteries (ZABs) and flexible ZABs (F-ZABs) equipped with M-PImPorCo/3D-G suggests the potential for catalytic oxygen reaction bifunctional applications. This work provides a new idea for the synthesis of Schiff-base porphyrin-based COF catalyst and its potential application to oxygen reaction catalytic energy storage devices.