Iron-Nitrogen-carbon (Fe-N-C) catalysts are promising substitutes for Pt-based catalysts in oxygen reduction reaction (ORR) for zinc-air battery. However, the sluggish kinetics of ORR on conventional Fe-N-C catalysts resulted from difficult desorption of *OH intermediate and the slow mass transfer significantly impede their practical application. Herein, a novel composite template-assisted strategy is proposed to prepare Fe-N4 sites on unusual fullerene-like curved surface featuring stretched Fe-N bonds and hierarchically porous structure (denoted as f-Fe-NC). With unique curved Fe-N4 sites and hierarchical porosity, f-Fe-NC exhibits an impressive half-wave potential (E1/2) of 0.91 V vs. RHE. Moreover, the mass activity of f-Fe-NC is nearly sevenfold of that of ordinary Fe-NC featuring planar Fe-N4 sites and microporous structure, and the turnover frequency of f-Fe-NC increases at exponent level compared to ordinary Fe-NC. Theoretical calculations demonstrate the reduced energy barrier of rate-determining step and favorable *OH desorption on f-Fe-NC because of the degradation of bond order of Fe-OH bond. Zinc-air battery based on f-Fe-NC exhibits a power density of 182 mW cm-2 and a specific capacity of 811 mAh g-1 at 10 mA cm-2, overtaking those of commercial Pt/C. Our study opens a new avenue for the rational design of electrochemically and structurally advanced ORR catalysts.