Deep learning-based methods for remaining useful life prediction (RUL) usually require the precondition that the training and test data obey the same distribution. In engineering applications, mechanical equipment is frequently under different working conditions, which can lead to significant differences in the distribution of collected data and difficulties in obtaining labels. This paper proposed a novel RUL prediction method based on transfer hybrid deep neural network to solve the above problems. Firstly, a degradation feature extraction strategy and a clustering hybrid feature screening strategy are proposed to enrich the information content of degradation features and obtain manual features with significant degradation trends. Then, a multi-stage shrinkage attention temporal convolution network is used to adaptively extract strongly expressive and information-rich deep features from the raw data. Next, a bidirectional convolutional gated recurrent unit based on bidirectional learning and convolutional operations is designed to achieve the fusion of manual and deep features and improve the quality of degradation features. Finally, the unsupervised domain adaptation strategy is used to reduce the differences in the distribution of degradation features between training and test data and to achieve feature alignment. This paper validates the effectiveness of the proposed method on six transfer tasks. The experimental results show that the RUL prediction effectiveness of the proposed method is better than other methods.