A full-waveform lidar system is able to record received signal continually for analysis. As it provides more information than the conventional discreted lidar, the waveform analysis is a key process to extract the implied information. The objective of this study is to analyze the received waveform as well as its parameter extraction. The waveform parameters include position, amplitude, and echo width. This study selects Gaussian distribution as a symmetric function and Weibull distribution as an asymmetric function to decompose the return waveform into a series of components. In data preprocessing, we use Gaussian smoothing to reduce the noise effect and differentiation of waveform to extract the initial echo peak. Then, we employ Trust Region algorithm to solve the non-linear optimization problem for Gaussian and Weibull distributions. The waveform attributes such as peak, amplitude, and echo width are further extracted by the extracted components. Finally, we calculate the residuals, RMSE, R-square between raw waveform data and fitting function for quality assessment. The test site is a mountain area located in the central part of Taiwan. The experimental data was acquired by Leica ALS60 system and was recorded in the format of LAS1.3. This study compares two different functions in waveform decomposition. The result of Weibull distribution is better than Gaussian distribution as this asymmetry distribution is more suitable for lidar waveform. However, the latter is relatively simple and easy to implement in the waveform analysis.