Metal-organic frameworks (MOFs) are regarded as effective precursors for the preparation of M-N-C oxygen reduction electrocatalytic materials. However, the structural collapse of MOFs during the pyrolysis limits their practical application. In this study, ZIF-67 was firstly modified by coating with the surfactant of F-127 and doping with Zn. After that, the modified Zn-ZIF-67@F-127 was pyrolyzed under argon atmosphere to fabricate the Co-N-C support with complete structure. By loading Pt on the surface of Co-N-C support, the Pt/Co-N-C composite catalyst for oxygen reduction reaction (ORR) was obtained. The ORR catalytic performances in the alkaline electrolyte were systematically studied. The experimental results show that the addition of F-127 can improve the morphological retention of Zn-ZIF-67@F-127 during the pyrolysis. More importantly, the onset potential, half-wave potential, and diffusion-limited current density of Pt/Co-N-C in O2-saturated 0.1 mol·L-1 KOH are 1.027 V, 0.836 V, and 5.51 mA·cm-2, respectively, which are similar to those of the commercial 20% Pt/C catalyst. The synergistic effect of Pt and Co-N-C not only exhibits a high selectivity and current density for the ORR four-electron pathway, but also shows a high stability approaching the commercial 20% Pt/C catalyst, and superior methanol resistance performance compared with the commercial 20% Pt/C in the chronoamperometry test.