Structural response data might be partially missing during acquisition and transmission by a structural health monitoring (SHM) system, affecting subsequent structural damage identification. Conventional deep learning methods require a substantial amount of data and have low training efficiency. With this in mind, this paper proposes a hybrid approach for data reconstruction and damage identification using an echo state network embedded with convolutional layers. The network has a training-free reservoir layer and focuses on historical information and multi-channel spatial features. As data redundancy occurs in most measured structural vibration responses, the extended Frobenius norm-principal component analysis method is applied to select valuable samples for updating the network, which greatly enhances the training efficiency. Experimental and numerical data from a physical bridge model is used to verify the data reconstruction capability and damage identification accuracy of the proposed method, and its performance is further compared with several existing deep learning methods.