The mechanisms for oxygen reduction reaction (ORR) on the metal-free phosphorus doped graphene (P-Gra) support are investigated using the density function theory (DFT) calculations. It is found that all the ORR species can be strongly adsorbed on the P-Gra except for the H2O molecule. Our calculation results show that all of the possible ORR elementary reactions could take place within a small region around the dopant and the ORR could proceed firstly by a 2e(-) process to form an OOH intermediate, which is followed by the 4e(-) process to break the O-O bond of OOH. Along this reaction path, the reduction of the second OH to H2O is the rate-limiting step with the largest barrier of 0.88 eV. To the best of our knowledge, this is the first theoretical investigation on the mechanisms for the entire process of the ORR on the P-Gra. (C) 2014 Elsevier B.V. All rights reserved.