Damage identification and prediction of concrete bridge structures are of great significance for early warning of structural damage states and service safety. In this paper, the acoustic emission signals under different damage states were obtained from a partial prestressed concrete cable-stayed bridge damage model test, and the damage degree of the test girders was identified and predicted by using a convolutional neural network. Firstly, the convolutional neural network architecture was built, and then the test beam was loaded to the limit state twice to obtain two sets of acoustic emission waveform signals for training, and the convolutional neural network recognition system was obtained after the training. The test beam was then loaded to the limit state again to obtain the test acoustic emission signals and fed into the convolutional neural network recognition system to predict the damage level and calculate the accuracy of damage recognition, and finally compared with the traditional BP neural network. The results showed that the damage degree of the test beam was successfully predicted based on a convolutional neural network with acoustic emission technology, and the combined accuracy of 3104 acoustic emission signals was as high as 96.71%; the network architecture with two convolutional layers plus two fully connected layers had the best prediction effect, and the accuracy was 6%~8% higher than that of the network with five convolutional layers plus five fully connected layers; compared with the traditional BP neural network, the convolutional neural network is 5%~10% more accurate than the traditional BP neural network, and can train and identify waveform signals of multiple dimensions without relying on the extraction of acoustic emission signal feature parameters.