This paper presents a novel fault diagnosis method for oil-immersed on-load tap changers (OLTC) to address the issue of limited diagnostic accuracy. The proposed method combines the analysis of mechanical vibration signals and high-frequency current signals from the contact pair, aiming to improve the precision of fault diagnosis. To begin with, an experimental platform was used to simulate the OLTC contact, enabling the collection of mechanical vibration signals and high-frequency current signals under different operational states. These signals underwent wavelet packet transform for denoising, followed by correlation analysis to investigate their interrelationships across various states. Features were then extracted and analyzed using ensemble empirical mode decomposition and the Hilbert–Huang transform. Subsequently, a support vector machine (SVM) was employed to analyze both the mechanical vibration signal and high-frequency current signal, facilitating the classification of the OLTC contact state. The results demonstrated that the joint analysis of electrical and mechanical signals provided a comprehensive representation of the actual contact state under different conditions. The SVM classification achieved an error below 10% in predicting the values of the two signal types, validating the efficiency and feasibility of the proposed fault diagnosis method for OLTC contacts. The findings presented in this paper offer valuable insights for on-site fault diagnosis of practical OLTCs.