Active sonar systems are one of the most commonly used acoustic devices for underwater equipment. They use observed signals, which mainly include target echo signals and reverberation, to detect, track, and locate underwater targets. Reverberation is the primary background interference for active sonar systems, especially in shallow sea environments. It is coupled with the target echo signal in both the time and frequency domain, which significantly complicates the extraction and analysis of the target echo signal. To combat the effect of reverberation, an attention and cepstrum analysis-guided network (ACANet) is proposed. The baseline system of the ACANet consists of a one-dimensional (1D) convolutional module and a reconstruction module. These are used to perform nonlinear mapping and to reconstruct clean spectrograms, respectively. Then, since most underwater targets contain multiple highlights, a cepstrum analysis module and a multi-head self-attention module are deployed before the baseline system to improve the reverberation suppression performance for multi-highlight targets. The systematic evaluation demonstrates that the proposed algorithm effectively suppresses the reverberation in observed signals and greatly preserves the highlight structure. Compared with NMF methods, the proposed ACANet no longer requires the target echo signal to be low-rank. Thus, it can better suppress the reverberation in multi-highlight observed signals. Furthermore, it demonstrates superior performance over NMF methods in the task of reverberation suppression for single-highlight observed signals. It creates favorable conditions for underwater platforms, such as unmanned underwater vehicles (UUVs), to carry out underwater target detection and tracking tasks.