Since the discovery of the oxygen reduction reaction (ORR) activity of the metal phthalocyanine, the great enthusiasm is ignited for searching the catalysts with low price replacing Pt-based catalysts. Here, the catalytic activities for the ORR on the Co or Ni doped MoS2 are studied by using density-functional theory (DFT). It is found that Co/MoS2 resembles FeN4 active site while Ni/MoS2 is similar with CoN4 active site. In details, for Co/MoS2, under the acid medium, the rate-determining step (RDS) is located at the second H2O formation with a barrier of 1.49 eV. While under the alkaline medium, RDS is the final OH- formation with the barrier of 0.94 eV. For Ni/MoS2, under the acid medium, the RDS is the same as that of Co/MoS2 with a barrier of 0.87 eV. However, RDS is the O formation with the barrier of 0.92 eV under the alkaline medium. Furthermore, due to the intact HOOH adsorption, it is expected that the 2e- ORR is present on Ni/MoS2, which means inferior activity compared with Co/MoS2. Our calculation demonstrates the ability to functionalize inert materials for the ORR and provides new materials to design effective Pt-free catalysts for fuel-cell technology. (C) 2015 Elsevier B.V. All rights reserved.