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The article presents the results on the adsorption of the dye methylene blue (MB) from an aqueous solution on a nanocomposite DDT (nanosized titanium dioxide in the anatase phase precipitated on diatomite) and its components – diatomite D and TiO2. The effect on adsorption of the pH of the solution, the dose of the adsorbent, the initial concentration, and temperature of the dye solution was studied. The equilibrium data were fitted to the Freundlich, Langmuir, and Dubinin-Radushkevich isotherms equations. The obtained parameters and correlation coefficients showed that the adsorption of the dye on D and TiO2 was best described by the Langmuir isotherm model, while the adsorption isotherm of MB on DDT – by the Dubinin-Radushkevich model. The MB adsorption data on DDT and D, obtained at different solution temperatures (20, 30, and 40°C) revealed irreversible adsorption, which increased with an increment of T. Thermodynamic parameters of the process were calculated. The negative values of the Gibbs free standard energy ΔGo show that the adsorption of MB on these adsorbents is spontaneous. Positive values of ΔHo, characteristic of the endothermic process, were relatively high, which indicates that the interaction between the sorbent molecules and the adsorbate was not only physical, but also chemical. The dye adsorption on TiO2 decreases with increasing the solution temperature; it is physical and exothermic in nature, ΔGo being positive and ΔHo negative. The values of the activation energy of adsorption Ea of MB on DDT, D, and TiO2, calculated according to the Dubinin-Radushkevich equation, was equal to 10.74, 11.78, and -2.68 kJ/mol, respectively, thus indicating the ion-exchange mechanism of the adsorption of MB by DDT and initial diatomite and physical adsorption by TiO2. A negative value of the activation energy for a sample of TiO2 means the absence of a potential barrier during adsorption of MB on this adsorbent.