Two-dimensional metal oxide sheets in HTiNbO5 and HSr2Nb3O10, cation-exchangeable layered metal oxides, were examined as solid acid catalysts. Exfoliation of HTiNbO5 and HSr2Nb3O10 in aqueous solutions formed colloidal single-crystal TiNbO5- and Sr2Nb3O10- nanosheets, which precipitated under an acidic condition to form aggregates of HTiNbO5 nanosheets and HSr2Nb3O10 nanosheets. Although esterification of acetic acid, cracking of cumene, and dehydration of 2-propanol were not catalyzed by original HTiNbO5 because of the narrow interlayer distance, which prevents the insertion of organic molecules, HTiNbO5 nanosheets functioned as a strong solid acid catalyst for the reactions. Nanosheets of HSr2Nb3O10 exhibited no or slight catalytic activity for these reactions. NH3 temperature-programmed desorption and H-1 magic-angle spinning nuclear magnetic resonance spectroscopy revealed that HTiNbO5 nanosheets have strong Bronsted acid sites, whereas HSr2Nb3O10 nanosheets do not.