Concerning the low accuracy and long running time of link prediction between dynamic network nodes, a dynamic network representation learning model using denoising AutoEncoder (dAE) as the framework and combining with Graph Convolutional Network (GCN) and Long Short-Term Memory (LSTM) network, named dynGAELSTM, was proposed. Firstly, the GCN was used in the front-end of this model to capture the feature information of the high-order graph neighborhood of the dynamic network nodes. Secondly, the extracted information was input into the coding layer of the dAE to obtain the low-dimensional feature vectors, and the spatio-temporal dependent features of the dynamic network were obtained on the LSTM network. Finally, a loss function was constructed by comparing the prediction map reconstructed through the decoding layer of the dAE with the real map, so as to optimize the model to complete the link prediction. Theoretical analysis and simulation experiments showed that compared with the model with the second-best prediction performance, the dynGAELSTM model had the prediction performance improved by 0.79, 1.19 and 3.13 percentage points respectively, and the running time reduced by 0.92% and 1.73% respectively. In summary, the dynGAELSTM model has higher accuracy and lower complexity in the link prediction tasks compared to the existing models.