Abstract: In allusion to familiar periodic narrowband interference and random white noise interference during the measurement of partial discharge signals of medium and high voltage cables, based on variational mode decomposition (abbr. VMD) and concave-convex threshold wavelet a method to denoise cable partial discharge signal was proposed. Firstly, By means of VMD the original signal was decomposed and reconstructed to perform the preliminary noise reduction. Secondly, the wavelet transform of concave-convex threshold was utilized to conduct further noise reduction. Applying the proposed method the noise reduction for the simulation signal and the measured signal was carried out and the obtained results were compared with the effects by traditional noise reduction method. Comparison results show that the noise reduction effect of the proposed method is better than those of traditional noise reduction method such as soft and hard threshold wavelet noise reduction and so on, meanwhile, the reservation effect of the characteristic of local discharge signal is better.