Abstract: This paper proposes a reverberation suppression method to enhance the detection capability of active sonar for underwater moving targets. Leveraging the strong correlation between multi-frame beamforming data of fixed-position active sonar, this method models the low-rank nature of reverberation using frequency-filtering tensor nuclear norm. The alternating direction method of multiplier is applied to decompose sonar data into a low-rank tensor containing stationary reverberation and a sparse tensor containing the echoes of moving targets. Due to the presence of reverberation fluctuations in the sparse tensor, this paper further suggests suppressing reverberation by exploiting the differences in weighted spatio-temporal density between reverberation fluctuations and moving target echoes. The effectiveness of the proposed method is validated using the collected shallow-water reverberation data. The experimental results indicate that the presented method can effectively suppress steady reverberation and reverberation fluctuations, thereby enhancing the detection capability of small targets using active sonar.