Future energy conversion that will replace fossil energy can be expected from oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) among high-performance bi-functional electrocatalysts. Herein, a hybrid material, CoFe@N-C/MNGF containing an N-doped carbon shell on the surface of CoFe alloy nanoparticles and three-dimensional (3D) mesoporous N-doped graphene foam with exposed active sites as an electron transfer substrate has been successfully synthesized to replace noble-metal catalysts. The electrocatalytic performance of CoFe@N-C/MNGF demonstrates better OER activity in 0.1 M KOH alkaline electrolyte with a remarkably low overpotential of 330 mV and low Tafel plot 130.6 mV⋅dec-1 at a current density of 10 mA⋅cm−2. And CoFe@N-C/MNGF has considerable ORR performance in terms of catalyst activity, electron transfer number and stability, which suggests its usefulness as a suitable replacement for ORR catalysts based on noble-metal used for cathode electrode of alkaline fuel cells. In particular, it showed a potential of 0.87 V in 0.1 M KOH alkaline electrolyte and low Tafel plot 71.7 mV⋅dec-1 at 5 mA⋅cm−2 and the number of electrons (n) transferred was estimated to be 2.1–3.61 at 0.15 to 0.35 V. Based on these results, this study provides new insights into a cost-efficient non-noble metal bi-functional electrocatalyst.