Aiming at the problem that the on-load tap-changer mechanical fault diagnosis is not accurate and potential mechanical faults cannot be found in time, this paper presents a novel method of on-load tap-changer mechanical fault diagnosis based on complementary set empirical mode decomposition (CEEMD), phase space reconstruction combined with gravitational search method (GSA) improved learning vector quantization neural network (LVQ). Firstly, the CEEMD is used to decompose the vibration signal into time-frequency domain. Then, the delay time and embedding dimension are determined through the C-C algorithm. The phase space of the inherent modal function (IMF) reflecting the characteristics of different frequencies is reconstructed, and the two feature quantities Lyapunov exponent reflecting the chaotic features and correlation dimension are extracted to form the feature vector. Finally, GSA is used to optimize the LVQ to solve the problem that the network is sensitive to the initial connection weight, thus enhancing the network performance in classifying and identifying the mechanical faults of the on-load tap-changer. The experimental analysis of the mechanical state of the on-load tap-changer proves the feasibility and effectiveness of combining phase space reconstruction with GSA-LVQ algorithm.