Aeroengines are the core components of an aircraft; therefore, their health determines flight safety. Currently, owing to their complex structure and problems associated with their various detection parameters, predicting the remaining useful life (RUL) of aeroengines is very important to ensure their safety and reliability. In this paper, we propose a new hybrid method based on convolutional neural networks (CNN), timing convolutional neural networks (TCN), and the multi-head attention mechanism. Firstly, an CNN-TCN model is established for multi-dimensional features, in which two layers of the CNN extract features of multi-dimensional input data, and the TCN process the timing features. Subsequently, the outputs of multiple CNN-TCNs are weighted using the multi-head attention mechanism, and the results are stitched together. Next, we compare the root mean square error (RMSE) and scores of various RUL prediction methods to show the superiority of the proposed method. The results showed that compared with previous research results, the RMSE and Score of FD001 decreased by 10.87% and 42.57%, respectively, whereas those of FD003 decreased by 14.13% and 58.15%, respectively.