This paper employs the finite element method to calculate the capacitance and inductance parameters of the transformer winding equivalent circuit under healthy conditions and three deformation types: radial displacement, radial deformation, and axial displacement. Using the equivalent circuit parameters of the deformed winding, the frequency response curves for the three deformation types of the transformer winding are obtained via the frequency response analysis (FRA). Nine key features, including the correlation coefficient, are extracted from the frequency response curves under different deformation conditions of the transformer winding to form the training and testing samples. A support vector machine (SVM) is used for transformer fault diagnosis, and the Bayesian optimization algorithm is employed to enhance the model’s performance. The training samples and testing samples, consisting of nine key features extracted from the frequency response curves under different deformation conditions, are used to train the model and classify fault types. The results indicate that the overall classification and recognition performance is ideal, especially for radial displacement and radial deformation types.