Abstract: When the active sonar of the motion platform performs non-cooperative target detection tasks, the target is often submerged in reverberation, and the space-time coupling effect generated by the motion of the sonar platform further reduces the detection performance of moving targets. The complex and ever-changing underwater reverberation and interference environment makes it difficult to obtain sufficient independent and identically distributed training samples, resulting in a sharp decline in the performance of traditional space-time adaptive processing (STAP) methods. This article proposes a reverberation suppression and low-speed target detection algorithm using weighted sparse recovery for moving sonar, which restores the high-resolution space-time spectrum of the target in a compressed sensing framework. The algorithm realizes low-speed target detection and parameter estimation in strong reverberation and noisy backgrounds. The data of the range cell to be detected is only utilized to avoid the impact of insufficient training data or lack of prior knowledge on reverberation suppression. The sparse STAP method is used to estimate weight vectors and construct a sparse weighted optimization problem to realize reverberation/noise suppression and target enhancement in the optimization process. A low complexity optimization solving method is designed, which greatly improves the computational efficiency and practicality of the algorithm. The simulation and lake experiment results have verified the superiority of this algorithm.