As a new type of riser connecting offshore platforms and submarine pipelines, steel catenary risers (SCRs) are generally subject to waves and currents for a long time, thus it is significant to fully evaluate the SCR structure’s safety. Aiming at the damage identification of the SCR, the acceleration time series signals at multiple locations are taken as the damage characteristics. The damage characteristics include spatial information of the measurement point location and time information of the acquisition signal. Therefore, a convolutional neural network (CNN) is employed to obtain spatial information. Considering the variable period characteristics of the acceleration time series of the SCR, a gated recurrent unit (GRU) neural network is utilized to study these characteristics. However, neither a single CNN nor GRU model can simultaneously obtain temporal and spatial data information. Therefore, by combining a CNN with a GRU, the CNN-GRU model is established. Moreover, the hyperparameters of deep learning models have a significant influence on their performance. Therefore, particle swarm optimization (PSO) is applied to solve the hyperparameter optimization problem of the CNN-GRU. Thus, the PSO-CNN-GRU (PCG) model is established. Subsequently, an SCR damage identification method based on the PCG model is presented to predict the damage location and degree by SCR acceleration time series. By analyzing the SCR acceleration data, the prediction performances of the PCG model and the PSO optimization capacity are verified. The experimental results indicate that the identification result of the proposed PCG model is better than that of several existing models (CNN, GRU, and CNN-GRU).