A transformer internal mechanical fault diagnosis method based on time-varying filtered empirical modal decomposition (TVFEMD) and sparrow search algorithm optimized least squares support vector machine (SSA-LSSVM) is proposed to identify the internal latent mechanical faults of transformers accurately and effectively. Firstly, the vibration signals from transformers with iron cores in different loose states are collected. Secondly, the vibration signals are decomposed by the empirical mode decomposition (EMD) which was improved by time-varying filtered to obtain multiple intrinsic mode function (IMF); i.e. modal components (IMFs). Thirdly, the correlation coefficient method was used to calculate the correlation between the IMFs component and the original vibration signal, and the sample entropy of the IMF component with the highest correlation is calculated to construct the feature vector set. Finally, with the highest diagnostic accuracy as the objective function, SSA is used to optimize the regularization parameters and kernel function parameters of LSSVM, the SSA-LSSVM diagnostic model is built. The vector set is diagnosed and identified by using the diagnosis model, and the diagnosis of latent mechanical faults inside the transformer core is realized. The experimental results show that the proposed method can effectively identify the latent mechanical faults inside the transformers, and the identification accuracy reaches more than 98%, which is more than 5% higher than the identification accuracy of the comparison algorithm, achieving the diagnosis effect of high identification accuracy.