The open-circuit fault signals of Vienna rectifiers exhibit non-stationary characteristics and are susceptible to sensor noise, reference offset, and load variations, which reduces the performance of traditional fault diagnosis methods. To address this, a fault diagnosis method based on significant feature extraction and improved random forests is proposed to improve the open-circuit fault diagnosis accuracy and robustness of Vienna rectifiers. First, the non-stationary characteristics and underlying mechanisms of open-circuit fault signals in Vienna rectifiers are analyzed. Then, an optimal discrete wavelet transform is defined to focuse on signal details, enabling multi-scale fault feature extraction. Meanwhile, considering the mutual effects of the features, the improved ReliefF algorithm is employed to select the most important features. On this basis, a robust accuracy-weighted random forest algorithm is utilized to map important fault features to fault categories. By performing noise robustness testing with the out-of-bag (OOB) data, the voting weights of decision trees are adjusted, thereby enhancing the accuracy and robustness of the fault diagnosis method. Finally, comparative experimental results show that the proposed method is robust to non-stationary variations and achieves an accuracy rate of 99.84%.