Based on the difference of the equivalent instantaneous magnetizing inductance of transformer under different operating conditions of transformer, this paper proposes to used the maximal overlapping discrete wavelet transform (MODWT) to extract effective fault characteristic parameters, and realize the detection of transformer windings with slight inter-turn short circuit faults and partial arc discharge faults. Firstly, the electric quantity of the transformer under various working conditions is extracted to obtain the equivalent instantaneous magnetizing inductance. The maximal overlapping discrete wavelet transform based on db4 wavelet function is selected for analysis, and feature quantities are extracted. The fault feature quantity is used as the training set and test set of the decision tree to realize the identification and classification of slight transformer winding faults. Finally, the simulation results show that the proposed algorithm can accurately detect and distinguish between magnetizing inrush currents, slight inter-turn short circuit faults and partial arc discharge faults.