In order to extract weak fault feature from vibration signals with noise, a method combining continuous wavelet transform with nonnegative matrix factorization with multiple constraints was put forward. Firstly, the continuous wavelet transform was adopted to transform the signal into time-frequency domain with the optimization of wavelet shape factor by wavelet entropy method. Secondly, the non-negative matrix factorization with sparsity and smoothness constraints was used to reduce the optimal coefficient matrix according to the fault characteristic shown by the matrix so as to extract fault feature with less noise. Finally, simulations and application data show that this approach is effectiveness of weak fault feature extraction and realizes the early fault diagnosis.