In this paper, we report on the discovery of an optical flare observed in the R band from the red-dwarf eclipsing binary CU Cancri, whose component stars are at the upper boundary of full convection (M1= 0.43 M⊙ and M2= 0.4 M⊙, where M⊙ is the solar mass). The amplitude of the flare is the largest among those detected in the R band (∼0.52 mag) and the duration time is about 73 min. Like flares observed on the Sun, quasi-periodic oscillations were seen during and after the flare. Three more R-band flares were found by follow-up monitoring. In total, this binary was monitored photometrically by using an R filter for 79.9 h, which has revealed an R-band flare rate of about 0.05 flares per hour. Together with other strong chromospheric and coronal activities (i.e. very strong Hα and Hβ emission features and an extreme ultraviolet and X-ray source), these detections indicate that it has very strong magnetic activity. Therefore, the apparent faintness (∼1.4 mag in the V band) of CU Cnc, compared with other single red dwarfs of the same mass, can be plausibly explained by the high coverage of dark spots.