Carbon quantum dots (CQDs) and two dimensional (2D) graphene sheets were prepared from formic acid by microwave mediated thermal method. Microwave irradiation followed by thermal evaporation of formic acid produces fluorescent CQDs. The fluorescence emission of CQDs in water can be tuned between 310 and 820 nm by changing the excitation wavelengths. These quantum dots are found to be sensitive towards hydrogen peroxide in aqueous medium due to quenching of fluorescence. The large area graphene sheets are formed on a solid substrate due to self assembly and 2D growth of CQDs. Graphene sheets modified glassy carbon electrode showed fast electron transfer kinetics for Fe(CN)63−/4− couple. Moreover, these modified electrodes can be used as a highly sensitive and selective metal free, non-enzymatic electrochemical sensor for hydrogen peroxide. The low detection limit was found to be 300 nM.