The effect of disorder on the electronic properties near the Mott transition is studied in an organic superconductor $kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br, which is systematically irradiated by X-ray. We observe that X-ray irradiation causes Anderson-type electron localization due to molecular disorder. The resistivity at low temperatures demonstrates variable range hopping conduction with Coulomb interaction. The experimental results show clearly that the electron localization by disorder is enhanced by the Coulomb interaction near the Mott transition.