Leakage current is an important indicator to characterize the performance of GIL internal insulator. In practical engineering, the acquisition of leakage current signal is often interfered by narrow-band signal and white noise signal, which affects the accurate evaluation of insulator performance. The common methods of leakage current denoising rely on empirical parameters and manual settings. In order to solve the above problems, singular value decomposition ( SVD) is improved by using singular value curvature spectrum to remove narrowband signal interference. Then, the positive and negative white noise groups are introduced, and the leakage current signal with white noise is decomposed by empirical mode decomposition ( EMD). In the decomposition process, the modal component is denoised, and the final modal component is the noiseless leakage current signal. The results of signal simulation and field measurement show that the proposed method can effectively denoise the leakage current of GIL insulator.