A novel cobalt-chelating polyimine (Co-PIM) containing an additional amine group is prepared from the condensation polymerization of diethylene triamine (DETA) and terephthalalehyde (PTAl) by the Schiff reaction. A Co, N-co-doped carbon material (Co-N-C), obtained from two-stage calcination in different gas atmospheres is used as the cathode catalyst of an anion exchange membrane fuel cell (AEMFC). The Co-N-C catalyst demonstrates a CoNx-type single-atom structure seen under high-resolution transmission electron microscopy (HRTEM). The Co-N-C catalysts are characterized by FTIR, XRD, and Raman spectroscopy as well. Their morphologies are also illustrated by SEM and TEM micrographs, respectively. Surface area and pore size distribution are found by BET analysis. Co-N-C catalysts exhibit a remarkable oxygen reduction reaction (ORR) at 0.8 V in the KOH(aq). From the LSV (linear-sweeping voltammetry) curves, the onset potential relative to RHE is 1.19–1.37 V, the half wave potential is 0.73–0.78 V, the Tafel slopes are 76.9–93.6 mV dec−1, and the average number of exchange electrons is 3.81. The limiting reduction current of CoNC-1000A-900 is almost the same as that of commercial 20 wt% Pt-deposited carbon particles (Pt/C), and the max power density (Pmax) of the single cell using CoNC-1000A-900 as the cathode catalyst reaches 361 mW cm−2, which is higher than Pt/C (284 mW cm−2).