This research focused on predicting of product quality of silicon steel sheets, cut by the pulsed laser machine. We used three-axis vibration signals, in time domain, measured at the specific point on the laser machine for analysis. Wavelet transformation was used to decompose each measured signal into several sub-signals with different frequency ranges. Then, the statistical features of sub-signals were extracted. Various Machine Learning (ML) tools or models, including support vector regression (SVR), random forest (RF), and extreme learning machine (ELM), were chosen for prediction. Selected significant features by Pearson's correlation analysis were adopted as the inputs, and the averaged kerf width of the straight cut of the silicon steel sheet, was chosen to be the output or target of ML methods. The performance comparison of three ML models was made based on the errors of training and testing scores. The results show that the random forest (RF) predictive model gives the lowest Mean Average Percentage Error (MAPE) and is the best model among these three models. This paper also discusses the strategy of selecting different wavelet features and effect of testing data size. In summary, the statistical features extracted from measured time-domain vibration signals during the laser cutting process is effective in predicting the kerf width of straight cut of the silicon steel sheet.