Data prediction and imputation are important parts of marine animal movement trajectory analysis as they can help researchers understand animal movement patterns and address missing data issues. Compared with traditional methods, deep learning methods can usually provide enhanced pattern extraction capabilities, but their applications in marine data analysis are still limited. In this research, we propose a composite deep learning model to improve the accuracy of marine animal trajectory prediction and imputation. The model extracts patterns from the trajectories with an encoder network and reconstructs the trajectories using these patterns with a decoder network. We use attention mechanisms to highlight certain extracted patterns as well for the decoder. We also feed these patterns into a second decoder for prediction and imputation. Therefore, our approach is a coupling of unsupervised learning with the encoder and the first decoder and supervised learning with the encoder and the second decoder. Experimental results demonstrate that our approach can reduce errors by at least 10% on average comparing with other methods.