This paper proposes a two-step method to build a light Convolutional Neural Network (CNN) for bearing fault diagnosis and Remaining Useful Life (RUL) prediction. The first step involves constructing a cell-based CNN with optimal cells and limited number of stacking cells. Differentiable Architecture Search is adopted for this purpose. The second step involves further reducing the connections in the built cell-based CNN by weights-ranking-based pruning. Results from experiments on the Case Western Reserve University data showed that the CNN with only two cells achieved a test accuracy of 99.969% and kept at 99.968% even after 50% connections were removed. The parameter size of the 2-cells CNN was reduced from 9.677MB to 0.197MB. The network structure was further adapted to achieve bearing RUL prediction and validated with the PRONOSTIA test data.