We proposed and studied an impact detection system based on a fiber Bragg grating (FBG) sensor array and multiple signal classification (MUSIC) algorithm to determine the location and the number of low velocity impacts on a carbon fiber-reinforced polymer (CFRP) plate. A FBG linear array, consisting of seven FBG sensors, was used for detecting the ultrasonic signals from impacts. The edge-filter method was employed for signal demodulation. Shannon wavelet transform was used to extract narrow band signals from the impacts. The Gerschgorin disc theorem was used for estimating the number of impacts. We used the MUSIC algorithm to obtain the coordinates of multi-impacts. The impact detection system was tested on a 500 mm × 500 mm × 1.5 mm CFRP plate. The results show that the maximum error and average error of the multi-impacts’ localization are 9.2 mm and 7.4 mm, respectively.