This paper proposes an impact localization system based on the fiber Bragg grating (FBG) array and minimum variance distortionless response (MVDR) beamforming algorithm. The linear FBG array, which contains seven FBG sensors, is used for detecting impact signals. Morlet wavelet transform is applied for extracting narrow-band signals of impact signals. According to the MVDR beamforming algorithm, the system realizes single-impact and multi-impact localizations. The localization system is verified on a 500 mm×500 mm×2 mm carbon fiber reinforced polymer (CFRP) plate for single-impact and multi-impact localizations. The average locating error and the maximum locating error are 6.8 mm and 9.9 mm, respectively.