Gravitational wave (GW) signals are often affected by noise interference in the detection system; in order to attenuate the impact of detector noise and enhance the waveform characteristics of the signal, this paper proposes a space-based GW signal denoising method that combines the Parrot algorithm (PO) with the improved wavelet threshold (IWT) to optimize the variational mode decomposition (VMD). To address the challenge of selecting the number of modes K and the penalty factor $\alpha$ in VMD, PO is introduced to select the optimal parameters, achieving a good balance between global search and local optimization. The components after modal decomposition are divided into preserved modal components and noise modal components, and the IWT is introduced to further denoise the noise modal components; finally, the signal is reconstructed to achieve the purpose of denoising the GW signal. The algorithm is verified by the GW simulation signal and the measured signal. The experimental results show that the algorithm is superior to other algorithms in the noise separation of GW signals, significantly improves the SNR, improves the detection accuracy of GW, and provides a new technical means for the extraction and analysis of GW signals.