In this work, the porous spinel-type of magnetic iron-manganese oxide nanocubes with a hollow structure deposited on the reduced graphene oxide nanoflakes (PMFMO@RGONF nanocomposite) is synthesized and examined as a non-noble electrocatalyst for hydrogen evolution reaction (HER) and oxygen reduction reaction (ORR). The Tafel slope of PMFMO@RGONF nanocomposite is about 107 mV dec(-1) in the 0.50 mol (L-1) H2SO4 solution and suggests the Volmer-Heyrovsky mechanism for HER. The results show that this electrocatalyst has an excellent stability (at least 10000 cycles) in the sulfuric acid solution. Hence, The LSV curve shows that the Pt(20%)/C has a better onset-potential than present electrocatalyst for HER but PMFMO@RGONF nanocomposite produces current density (j) of 300 mAcm(-2) at overpotential (eta) of -721 mV (eta 300 = -721 mV(vs. Ag/AgCI)) which is smaller than Pt(20%)/C (eta 300 = -802 mV). The PMFMO@RGONF nanocomposite as an electrocatalyst follows four electrons mechanism for ORR in 0.10 mol L-1 KOH. As an important result, after addition of methanol into the electrolyte, this electrocatalyst is stable for a long time (at least 10000s) while the catalytic activity of Pt (20%)/C is quickly lost in the presence of methanol. (C) 2018 Elsevier Ltd. All rights reserved.