In response to the increasing complexity of degradation characteristics in aircraft engines, which leads to the low accuracy of traditional deep learning methods in predicting the remaining useful life (RUL), this paper proposes a stacked bidirectional long short-term memory network (BiLSTM) based on a scaled dot-product attention mechanism to improve prediction accuracy. Firstly, two layers of BiLSTM are stacked together, and then a dot-product attention layer is inserted between the two layers of BiLSTM. A scaling factor is introduced in the computation of attention weights to avoid gradient issues. Finally, a linear mapping layer is added before the attention layer to better adapt to attention computation. To validate the effectiveness, the turbine engine dataset provided by NASA is used for experimentation. The experimental results demonstrate that for complex datasets, the proposed method reduces the root mean square error by 36.5%, 31.7%, 23.4%, and 32.2% compared to convolutional neural networks (CNN), long short-term memory networks (LSTM), CNN-LSTM, and gated recurrent unit (GRU), respectively, effectively improving the prediction accuracy of the model.