To achieve denoising of pipe leak acoustic signal under the conditions of extremely low signal-to-noise ratio, based on the signal correlation among multiple channels, a correlation coefficient matrix is presented to determine the modes obtained by using the variational mode decomposition. For the leak signals under different conditions, the quality evaluation index for denoising that does not rely on the real value is presented to use it as the object function of the multi-objective grey wolf optimization algorithm. The best mode number K and penalty factor η of the variational mode decomposition are determined according to the Pareto front, achieving adaptive denoising under multiple conditions. An experimental rig of gas pipe leak under multiple conditions is established to evaluate the effectiveness of the proposed method under multiple conditions and with different signal to noise ratios (-8~ 4 dB) of input signals. The results show that this method can effectively suppress noises. Even in the case of -8 dB, the signal-to-noise ratio of denoised signals is amplified by more than 2. 84 dB. Compared with the method based on single-objective optimization, at -8 dB, the signal-to-noise ratio and correlation coefficient of the new method are increased by 3. 65 dB and 31. 26% , respectively.