Knowing remaining useful life (RUL) of bearing can better ensure the safe and effective production activities. The feature learning performance of traditional prognosis models is influenced by the noise characteristics of the original vibration signal with ease. In view of the limitation, a RUL prediction approach on the strength of the multi-scale convolutional neural network with Squeeze-and-Excitation mechanism (MsCNN_SE) is proposed. Continuous wavelet transform (CWT) is used to extract time-frequency characteristics from original signals, which are considered as the input of MsCNN_SE model for RUL prediction. The designed multi-scale network can extract richer local information and alleviate the phenomenon of gradient disappearance by increasing the network width. To reduce the interference of redundant features, the Squeeze-and-Excitation (SE) mechanism is introduced to enhance the correlation between features. Compared with the traditional convolutional neural network, the MsCNN_SE model can maintain global and local information at the same time. The validity of the proposed approach is verified by experimental data, and it shows a good prediction performance.