The weak binding force of oxygenated species on metal-nitrogen-carbon catalytic sites severely restricts the catalytic activities towards the oxygen reduction reaction. Herein, we report a one-step method for the in-situ immobilization of poly(p-phenylenediamine-formaldehyde) on the Co, Zn-zeolitic imidazolate frameworks to construct pyrrolic/graphitic N-rich Co-N-C structures. Pyrrolic/graphitic N species derived from poly(p-phenylenediamine-formaldehyde) reduce the electron localization around the Co centers for increasing the charge polarization between Co and neighboring N atoms, leading to strengthening the adsorption of oxygenated species and improving the intrinsic activity. What's more, pyrrolic/graphitic N-rich Co-N-C structures conserve the characteristics of zeolitic imidazolate frameworks-derived catalysts, such as, large surface area, high pore volume, and atomically dispersed Co species, to fully expose efficient Co-N-C catalytic sites. Hence, the resultants as precious-metal-free catalysts demonstrate excellent catalytic activities in acidic and alkaline media, and are even superior to that of the state-of-the-art Pt/C catalyst in an alkaline environment. Moreover, doping S atoms into carbon lattice induces the asymmetric electron and spin densities of adjacent carbon atoms for providing for more oxygen adsorption sites and facilitating the formation of the OOH species, resulting in synergistically boosting the ORR activity in an acidic environment with efficient Co-N-C sites.