Here, a new hybrid material consisting Co(OH)(2) magnetic nanoflake (MNF-Co(OH)(2)) grown on reduced graphene oxide nanoflake (MNF-Co(OH)(2)@RGONF) was synthesized as an excellent bi-functional electrocatalyst for the oxygen evolution reaction (OER) and oxygen reduction reaction (ORR) in alkaline media, by a facile and inexpensive technique. The onset potential, current density at 2.025 V (vs. BEE), and Tafel slope of OER in 1.0 mol L-1 KOH for MNF-Co(OH)(2)@RGONF modified glassy carbon electrode (MNF-Co(OH)(2)@RGONF/GCE) were about 1.505 mV (vs. RHE), 227 mA cm(-2) and 63 mV dec(-1), respectively. So that the current density and Tafel slope of this electrocatalyst are better than commercial IrO2. Furthermore, it was concluded that MNF-Co (OH)(2)@RGONF/GCE due to four-electron transfer mechanism, an overvoltage about 775 mV (vs. RHE), better durability and stronger resistance rather than Pt/C (20%) at 0.436 V in KOH 0.10 mol L-1 (with the addition of methanol to electrochemical cell), has a high catalytic activity for ORR.