A family of isoreticular metal-organic frameworks, based on the UiO-66 structure with NH2-, OH-, HSO3-, and NO2-substituted terephthalic acid, are synthesized and tested as catalysts in liquid-phase oxidation of propylene glycol (PG) with hydrogen peroxide and compared with the catalytic performances of unsubstituted UiO-66. The obtained materials are characterized by X-ray diffraction, FT-IR, thermogravimetric analysis (TGA), nuclear magnetic resonance spectroscopy (1H NMR), and Fourier-transform infrared spectroscopy (FT-IR) of adsorbed CO and scanning electron microscopy (SEM) methods. Hydroxyacetone (HA) is the main product over all X-UiO-66 catalysts under the reaction conditions used. The nature of substituent drastically affects the PG conversion and the oxidant utilization efficiency. The presence of electron-withdrawing groups in the organic linker leads to preferential heterotic activation of H2O2, whereas the increase of electron density around Zr active sites, promoted by electron-donating groups, enhances the unproductive homolytic oxidant decomposition. The insertion of NO2 group results in almost double increase in the HA yield (15.5 vs. 8.8%) and hydrogen peroxide utilization efficiency (98 vs. 36%) in comparison with the reaction catalyzed by H-UiO-66. The NO2-UiO-66 can be recycled without the loss of the catalytic activity and preserves its structure after the catalytic cycle.