To address the issue of insufficient universality in current partial discharge signal denoising methods, a method based on variational mode decomposition (VMD) is proposed, which achieves adaptive parameter optimization and incorporates discrete wavelet transform (DWT) for denoising. To achieve adaptivity for the method, an optimization model for the best parameter of VDM is established, which adopts a combined “soft threshold” and “hard threshold” approach for kurtosis screening and takes the minimization that differs the denoised signal from the original signal as the objective function, and the Northern Goshawk Optimization algorithm is applied to realize the optimization. The effectiveness of the method is verified through tests on both simulated data and experimental data. The simulated data encompass partial discharge pulses of four typical waveform expressions as well as strong interference consisting of white noise and two narrowband interferences. After processing by the proposed method, the signal-to-noise ratio is improved from −18.46 dB to 12.54 dB. The experimental data are acquired using a partial discharge ultrasonic signal acquisition device developed by the authors in scenarios with high environmental similarity to actual engineering noise conditions, which can well reflect on-site engineering interference and hardware circuit noise interference. The partial discharges are generated by true-type defects, avoiding deviations from actual insulation defects that may occur with standard partial discharge specimens. After processing by the proposed method, the acquired data achieve a signal-to-noise ratio improvement of 38.19 dB and a noise suppression ratio of 9.88 dB, and yield waveforms with distinct features that are consistent with the typical partial discharge signal features of the defect. The effectiveness, necessity, and performance advantages of each step of the proposed method are validated through comparative analysis with the processing results of DWT, EMD (Empirical Mode Decomposition)-DWT, and PSO (Particle Swarm Optimization)-VMD-DWT algorithms.