In order to predict remaining useful life（RUL） of bearings, the wavelet-spectral kurtosis analysis method is used. Firstly, the bearing vibration sequence signal is decomposed by wavelet packet, the spectral kurtosis is chosen to determine the fault characteristic frequency band and reconstructed the signal. Then, determine whether the bearing is faulty according to its spectral characteristics. Lastly, the incipient fault point（IFT） of the bearing vibration sequence signal is determined. On this basis, the one-dimensional deep separable convolutional neural network with attention mechanism is used for the extraction of bearing vibration signal features. Compared with traditional convolutional neural networks, deep separable convolutional layers can reduce the number of network training parameters and speed up network training. The experimental results show that the introduction of the attention mechanism enables the network to focus on the key features in the signal, assign greater weight to important features, avoid the shortage of manual processing features, and facilitate effective feature extraction. The final prediction results are better than common data-driven methods such as SVR, CNN, and RNN.