[en] We report the X-ray irradiation effect on the superconductivity in the organic superconductor κ-(BEDT-TTF)₂Cu[N(CN)₂]Br which is located nearby the Mott insulator-metal transition. The superconducting transition temperature T_c decreases almost linearly with increasing irradiation dose. The suppression rate of T_c for irradiation dose is larger than that reported so far in κ-(BEDT-TTF)₂Cu(NCS)₂. The difference in the suppression of T_c between two organic superconductors might result from the different anion molecules, which may be altered by the X-ray irradiation, and the different strength of the electron correlation.