Aiming at low response and weak measurement ability of the all-fiber optic leakage current sensor in the ship power network, a denoising method based on the combination of VMD(variational modal decomposition) and MF(morphological filtering) was proposed to improve the ability of weak current measurement. The hunter-prey optimization algorithm was used to search for the optimal combination of model number and quadratic penalty term based on the minimum entropy of the Hilbert spectrum, and the intrinsic mode functions component were obtained by completing the variational mode decomposition. The practical modal function component was determined by setting the correlation coefficient threshold to complete the signal reconstruction. The structure factor and scale coefficient of MF were determined by the hunter-prey optimization algorithm with the signal-to-noise ratio as the fitness function. The reconstructed signal was subjected to time-domain denoising processing to further denoise in the leakage current signal. This method significantly improve the signal-to-noise ratio and reduce the minimum mean square error to the existing filtering methods by simulation analysis and experimental verification. The leakage current resolution is achieved to 3mA with the proposed denoising algorithm.