Full-waveform LiDAR is a rising technique in the field of remote sensing. Compared with traditional LiDAR, it can digitize all the back-scattering pulses. More abundant attribute of targets shall be obtained by waveform decomposition, which is the core content of full-waveform lidar data processing. A waveform decomposition method based on global convergent LM was proposed. Waveform was fitted and optimal solutions of components′ parameters were obtained by introducing global convergent LM. Decomposition of complex overlapping waveform components was realized by iterative peaks detection. The experimental results on GLAS, LVIS and Lite Mapper-5600 waveform data prove that, the decomposing results are more robust than traditional LM and proposed method is practical as it is suitable for satellite, airborne large footprint size and airborne small footprint size waveform data.