Graphitic carbon nitride (g-C3N4) has proved to be a promising heterogeneous photocatalyst in the visible range. It can be used, among others, for the oxidative conversion of environmentally harmful nitrophenols occurring in wastewater. However, its photocatalytic activity needs to be enhanced, which can be achieved by modification with various dopants. In our work, copper-modified g-C3N4 was prepared by ultrasonic impregnation of the pristine g-C3N4 synthesized from thiourea. The morphology, microstructure, and optical properties of the photocatalysts were characterized by XRD, FT-IR, DRS, SEM, XPS, and TEM. DRS analysis indicated a slight change in both the CB and the VB energies of Cu/g-C3N4 compared to those of g-C3N4. The efficiency of the photocatalysts prepared was tested by the degradation of nitrophenols. Copper modification caused a sevenfold increase in the rate of 4-nitrophenol degradation in the presence of H2O2 at pH = 3. This dramatic enhancement can be attributed to the synergistic effect of copper and H2O2 in this photocatalytic system. A minor Fenton reaction role was also detected. The reusability of the Cu/g-C3N4 catalyst was demonstrated through five cycles. Copper-modified g-C3N4 with H2O2 proved to be applicable for efficient visible-light-driven photocatalytic oxidative degradation of nitrophenols.