Solid acid catalysts based on graphite-like carbon material "Sibunit-4" have been developed to be utilized in the one-pot process of 5-hydroxymethylfurfural production from cellulose using oxidation and subsequent oxidation-sulfonation methods. The samples of oxidized carbon have been produced via oxidation of the carbon's surface by water solutions of nitric acid or by wet air mixture; for oxidized-sulfonated samples to be produced oxidized carbons have been additionally sulfonated in fuming sulfuric acid at 200 °С. The catalysts developed have been investigated by methods of low-temperature nitrogen absorption and titration with NaOH and also tasted in the one-pot hydrolysis-dehydration of mechanically activated cellulose under hydrothermal conditions of 180 °С. The total amount of acidic groups (sulfo, carboxyl, lactone, and phenolic) for oxidized samples is comparable and for the oxidized-sulfonated is 1.5-2 times higher than the amount of acid groups in the Sibunit sulfonated at 200 ° C. The activity of the catalysts with respect to sulfonated samples at 150 ° C and 200 ° C is comparable. The yields of 5-HMF and glucose ranges of 17-20% and 38-42%, respectively.