Aiming at the vibration signals are nonlinear and time-varying since the no-load closing of a transformer, a fault feature extraction method that combines local mean decomposition（LMD）and Hilbert marginal spectrum energy entropy is proposed. Several product function(PF) components that reflect the mechanical state information of operating process are extracted by LMD. The top 6th order components that are selected based on the energy distribution and correlation coefficients, are transformed by Hilbert transform, and their marginal spectrum energy entropy are calculated as the feature quantities. The Fire?Works Algorithm（FWA）is used to optimize the support vector machine classifier to identify the different states of transformer winding. The experimental results show that the features based on LMD-Hilbert marginal spectrum energy entropy extraction can accurately reflect the fault characteristics，and the FWA-SVM diagnosis method has a good effect on in the case of a small number of samples.