Highly-acidic graphene oxide in the presence of hydrogen peroxide was found to act as an efficient metal-free heterogeneous catalyst for oxidation of sulfides to sulfones under mild and neutral condition. Several factors such as catalyst amount, solvent, and reaction time pertaining to achieve the reactivity were also discussed. Sulfone formation increased with an increase in hydrogen peroxide concentration, temperature, and catalyst amounts. The uniqueness of this catalyst lies in its stability, cost-effective, ease in removal at the end of reaction, and chemoselective oxidation of alkyl and aryl sulfides to the corresponding sulfones. The catalyst is recyclable for at least four times only with the little reduction in oxidation of sulfides. Reaction kinetics was found to be pseudo-first order and the calculated activation energy was 32.11 kJ/mol.