To decompose asymmetric full-waveform LiDAR data with unknown number of components, a full-waveform LiDAR decomposition method was proposed based on skew-normal distribution and reversible-jump Markov Chain Monte Carlo (RJMCMC) algorithm, which can automatically determine the numbers of components. First, the energy function was used to describe the differences between the actual waveform and the ideal waveform that obeyed the skew-normal distribution, and the likelihood function was defined by Gibbs distribution. Second, the parameter models of the ideal waveform were established using the prior distribution. Then the Bayesian paradigm was followed to build the ideal waveform model. Third, an RJMCMC algorithm was designed to determine the numbers of components and decompose the waveform. The proposed algorithm was used to decompose ICESat-GLAS waveform data in various typical regions. Experimental results indicate that the cross-correlation of the true data and the result is up to 98.9%. The proposed method can not only fit the skewed waveform data and normal waveform data, but also more accurately determine the number of components in comparison to other methods. It can realize the accurate decomposition of full-waveform LiDAR data, and the decomposition result is consistent with the corresponding elevation information.