Partial discharge (PD) detection is significant for insulation condition evaluation of electrical equipment. However, it often happens that the PD signals are submerged by interferences, which will cause the inaccurate detection results. In this paper, we propose a PD detection method based on double-density dual-tree complex wavelet transform (DD-DT CWT) and singular value decomposition (SVD) to solve this problem. The denoising method based on DD-DT CWT has better performance in both removing interferences and retaining features of PD signals. The inner product of the singular value matrix obtained by applying SVD to denoised high-frequency wavelet coefficient matrix can concisely represent the complexity of the tested signal, which can be used as a basis to judge the existence of the PD signal. Besides, Otsu algorithm is introduced to calculate the threshold to locate the appearance time of the PD signal. Experimental results show that the proposed method can detect the PD signal with the accuracy rate of 77.8% when PD signals are submerged by noises, while the traditional method cannot detect the existence of the PD signal. In addition, only the method proposed in this paper can detect the appearance time of the PD signal with the accuracy rate of 97.2%.