Aiming at the difficulty of predicting the remaining useful life （RUL） of a rolling bearing under the two modes of performance degradation gradual failure and sudden failure， a RUL prediction method is proposed combining convolution neural networks （CNN） with long short term memory （LSTM） neural networks. Firstly， the original vibration signal of the rolling bearing is transformed by fast Fourier transform （FFT）， and then the frequency domain amplitude signal obtained by pre-processing is normalized as the input of CNN. CNN can adaptively extract local intrinsic useful information， learn and excavate deep features， thus avoiding the drawbacks of traditional algorithms that require a lot of experts' experience. Then deep features are input into LSTM neural networks to construct trend quantification health indicators to determine the failure threshold. Finally， the moving average method is used to smooth out the local oscillation， and then the polynomial curve fitting is used to predict the future failure time and realize the RUL prediction of rolling bearings. The experimental results show that， under the two modes， the trend quantification health indicators constructed by the proposed method all have good monotonous trend and prediction results， which can better approach the real life values.