 The design of bifunctional non-precious metal catalyst with good ORR and OER activity is of great significance for the development and commercialization of fuel cells. However, the sluggish and strong irreversible nature of the oxygen electrochemical kinetics makes it difficult to manufacture single bifunctional material. Therefore, we prepared a bifunctional catalyst (Co3O4/N-rGO) with different particle diameters through a one-pot synthesis method, and studied the dependence of the electrocatalytic performance of the catalyst on the particle size of Co3O4. The results showed that Co3O4/N-rGO with 27–31 nm particle size prepared by using N-rGO as the carrier, cobalt acetate concentration of 0.075 M, hydrothermal temperature of 190 °C, and hydrothermal time of 3 h takes a 4e-reaction pathway, which exhibited better ORR and OER activity, excellent current stability and methanol tolerance than JM 20% Pt/C and JM 5% RuO2/C.