Among the different types of fuel cell technologies, direct methanol fuel cells (DMFCs) are the most suitable for mobile and portable electronic applications. The development of cost-effective, active, and stable catalysts, able to substitute Pt or allow reducing the amount of it in low temperature fuel cell anodes is still in progress. In our previous works [1, 2] it has been shown that the graphene supported platinum-cobalt catalysts prepared by means of microwave synthesis enhance electrocatalytic activity towards the oxidation of borohydride and ethanol in an alkaline medium and are promising anode materials for direct borohydride fuel cells (DBFCs) and ethanol fuel cells (DEFCs). In this study investigation of activity of the graphene supported platinum-cobalt catalysts with the different Pt:Co molar ratios, fabricated by the rapid microwave heating method, towards the electro-oxidation of methanol in an acidic medium is presented. The Pt-Co/GR catalysts with the Pt:Co molar ratios equal to 1:3, 1:6, 1:20, 1:50 and 1:60 were prepared by microwave-assisted heating of required amounts of Pt(IV), Co(II) and ethylene glycol at a temperature 170 oC for 30 min. For comparison, the graphene supported Pt catalyst was also prepared at 170 oC for 30 s. The Pt loading in the synthesized catalysts was near 0.1 mg Pt cm-2. The electrochemically active surface areas of Pt in the synthesized Pt/GR and Pt-Co/GR catalysts were determined from the cyclic voltammograms of the mentioned catalysts recorded in a deaerated 0.5 M H2SO4 solution at a sweep rate 50 mV s-1 by calculating the charge associated with hydrogen adsorption (220 µCcm-2) and are 0.7 cm2 for Pt/GR and 5.2, 2.9, 1.6, 1.0 and 0.5 cm2for the Pt-Co/GR catalysts with the Pt:Co molar ratios equal to 1:3, 1:6, 1:20, 1:50 and 1:60, respectively. Values of the electrochemically active surface areas of the investigated Pt-Co/GR catalysts are 1.4-7.5 times higher than those of the Pt/GR catalyst. Electrochemical properties of Pt-Co/GR were investigated towards the electro-oxidation of methanol in acidic medium by means of cyclic voltammetry and chronoamperometry and compared with those of the bare graphene supported Pt catalyst. It has been determined that the Pt-Co/GR catalysts with the Pt:Co molar ratios equal to 1:3, 1:6, 1:20 exhibit an enhanced electrocatalytic performance for methanol electro-oxidation as compared with that of bare graphene supported platinum catalyst. Methanol oxidation current density values are ca. 2.1-3.2 times higher at the Pt-Co/GR catalysts with the above mention Pt:Co molar ratios than those at the Pt/GR catalyst. Highest electrocatalytic activity towards the electro-oxidation of methanol in acidic medium shows the graphene supported Pt-Co catalyst with the Pt:Co molar ratios equal to 1:3 and 1:6 as compared with that of catalysts with higher Pt:Co molar ratios and Pt/GR. These results obtained show that the Pt-Co/GR catalysts with the different Pt:Co molar ratios could have promising future as catalysts for DMFC.