We report here the discovery of an optical flare observed in R band from the red-dwarf eclipsing binary CU Cnc whose component stars are at the upper boundary of full convection (M1=0.43 and M2=0.4M0, M0 is the solar mass). The amplitude of the flare
is the largest among those detected in R band (~0.52mag) and the duration time is about 73 minutes. As those 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 R filter for 79.9 hours, which reveals a R-band flare rate about 0.05 flares per hour. These detections together with other strong chromospheric and coronal activities, i.e., very strong H_alpha and H_beta emission features and an EUV and X-ray source, indicate that it has very strong magnetic activity. Therefore, the apparent faintness (~1.4 magnitude in V) of CU Cnc compared with other single red dwarfs of the same mass can be plausibly explained by the high coverage of the dark spots.
