The single atom or cluster catalysts supported by two dimensional (2D) materials are the most promising low cost alternatives to the pure Pt catalyst for the oxygen reduction reaction (ORR). In this work, we have investigated the ORR mechanism on the g-C3N4 supported single Ce atom (i.e., Ce/g-C3N4) and cluster (i.e., CexPt6-x/g-C3N4) theoretically. Our study shows that Ce atom can be tightly bound to the g-C3N4 substrate and the presence of Ce atom is extremely favorable for the anchoring of CexPt6-x clusters on the substrate. The Ce/g-C3N4 shows similar ORR catalytic activity compared with bulk Pt. The reaction is a four-electron process. The most favorable pathway is the hydrogenation of OOH to form O + H2O. On the other hand, CexPt6-x/g-C3N4 (x = 0, 1, 3, 5, 6) is thermodynamically stable and shows a very different catalytic behavior. Particularly, the working potential is predicted to be 0.50 V for Ce3Pt3/g-C3N4, implying that it is a potential ORR catalyst.