A novel copper doped graphitic carbon nitride (Cu-C3N4) was successfully synthesized and used as an effective Fenton-like catalyst. Cu-C3N4 was characterized by scanning electron microscopy, surface area analyzer, Fourier transform infrared spectroscopy, X-ray diffractometer, and X-ray photoelectron spectroscopy. Effect of process parameters including catalyst dosage, hydrogen peroxide (H2O2) concentration, solution pH, and initial methylene blue (MB) concentration was investigated to evaluate catalytic performance. The pseudo first-order kinetic model was used to describe the catalytic process. The enhancement of MB degradation is observed assisted by ultrasound. MB degradation of 96% is obtained within 30 min in Cu-C3N4/H2O2/ultrasound system, and the corresponding rate constant is 0.099 min−1. Effective MB degradation is obtained over a broad pH range (3.3–9.9). The catalytic mechanism is examined by ultraviolet-visible spectra, quenching test, and electron spin resonance determination. The dominant mechanism of MB degradation is ascribed to the ultrasonic H2O2 activation by Cu-C3N4 for hydroxyl radical generation. Cu-C3N4 has good reusability and is effective to degrade rhodamine B and acid orange 7. This work not only contributes to the field of wastewater treatment, but also provides insights into the synthesis of Fenton-like catalysts. The results manifest that Cu-C3N4 is a promising Fenton-like catalyst for dye degradation in the field of environmental pollution remediation.