The mechanical vibration or rotation of the target or its components produces the micro-Doppler effect, which plays an important role in target classification and recognition. However, the micro-Doppler effect of many objects in the environment (such as wind turbines, air conditioners, etc.) is like time-varying clutter to the radar system, leading to false alarms. In this paper, aiming at the problem that micro-Doppler clutter may interfere with passive radar target detection, a micro-Doppler clutter suppression method based on the improved Sparsity of Adaptive Matching Pursuit (SAMP) is proposed. Considering the sparse characteristics of the micro-Doppler clutter, this problem can be transformed into a sparse signal representation problem, and the purpose of suppressing the micro-Doppler clutter is achieved by separating the signal. Compared with the original SAMP algorithm, the improved SAMP algorithm can quickly stop iteration after the residual reaches the adaptive threshold. Simulation and measured data verify the effectiveness of the proposed method.