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Summary A novel vibration‐based structural health monitoring (SHM) approach that uses two‐dimensional deep convolution neural networks (CNN) is introduced. The CNN extracts the features from acceleration response histories and drastically reduces the dimension of response history to make damage state classification possible with limited number of acceleration measurements. The proposed method was validated, and its applicability and efficiency were demonstrated using vibration response data recorded during the shake‐table testing of a one‐fourth–scale model of a reinforced concrete highway bridge. The proposed method predicted predefined damage states with 100% accuracy using recorded (acceleration) vibration response data. The method was shown to be robust and sensitive to very small changes in structural condition. It is also noted that the CNN‐based SHM method is scalable to any large number of damage states (including extent and location) with suitable network training. The required training data may be generated analytically using a nonlinear finite element model.