Online partial discharge (PD) detection for power cables is one reliable means of monitoring their health. However, strong interference by white noise poses a major challenge in the process of collecting information on partial discharge signals. To solve the problem whereby the wavelet threshold estimation based on sample entropy falls into the local optimal and the wavelet noise reduction makes it difficult to process detailed information, we propose a partial discharge signal noise reduction method based on a combination of improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and discrete wavelet transform (DWT) with multiscale sample entropy (MSE). Firstly, the ICEEMDAN method was used to decompose the original sequence into multiple intrinsic mode components. The intrinsic mode function (IMF) components were grouped using the mutual information method, and high-frequency noise was eliminated using the kurtosis criterion. Next, an MSE model was established to optimize the wavelet threshold, and wavelet noise reduction was applied to the effective component. The ICEEMDAN-MSE-DWT method can retain effective information while achieving complete denoising, which alleviates the problem of information loss that occurs after denoising using the wavelet method. Lastly, as shown by our simulation and experimental results, the proposed method can effectively realize noise reduction for power cable partial discharge signals, thus providing an effective method.