Underwater Acoustic signal denoising is encountering high demand due to the extensive use of acoustic in a lot of underwater applications. Underwater acoustic noise (UWAN) has a high effect on the quality of the acoustic signal therefore, it is always preferred to use a de-noising filter to remove it. In this paper, we propose a filter that utilizes a Complex wavelet transform (CWT) to remove UWAN and help improve the signal-to-noise ratio (SNR) of the detected acoustic signal. CWT is nearly shift-invariant and offers a good directionality in contrast to normal wavelet transform (DWT). The proposed method was tested using a real recorded UWAN for three depths from the Tigris River. The proposed method was compared with a more conveniently used discrete wavelet transform. The test included using Two signals: fixed frequency and linear modulation signal. De-noising was performed using a soft thresholding technique based on level-dependent threshold estimation. The proposed method showed supreme performance in terms of SNR and root mean square error (RMSE). When the input signal was 5.9 dB and -13.2 dB for SNR and RMSE respectively, the results were 10.9 dB for SNR and -15.7 dB for RMSE in the case of fixed frequency.