In order to solve the problems such as poor anti-noise， insensitivity to incipient damage and low performance of multiple damage localization by using modal shapes or their derivatives， a multi-damage identification method for composite laminates based on low-rank property of vibration modes and sparse damage distribution is proposed. Here， Laplacian of Gaussian （LoG） filter is adopted to evaluate the noise-robust curvature of modal shapes. Meanwhile， robust principal component analysis is utilized to examine the local damage-caused features of modal shape curvatures for damage localization. In addition， a damage localization index is developed to integrate the damage evidences of multiple modal shapes. Finally， the effectiveness of the proposed method is verified by numerical simulations and experimental data of composite laminates with damage. The results show that this method can accurately pinpoint the multiple small area damage in composite laminates without reference information on pristine state.