Because of the natural broadening, Doppler broadening, and collision broadening of spectral lines, multiple adjacent peaks in the absorption spectrum signal of mixed gas with multiple components are often overlapping, which makes the qualitative or quantitative analysis of hybrid gas composition difficult. Existing methods have deficiencies in obtaining a prior knowledge, accuracy, and computational efficiency. An overlapping peak separation algorithm for absorption spectra is proposed in this paper, which can identify, locate, and parse independent peaks overlapped in the spectral signal by combining the multiscale observation of wavelet and the self-similarity measure of fractal. Firstly, spectral signal with overlapping peaks was transformed to the time-frequency domain by wavelet, so we can analyze it in light frequency and scale domain. Secondly, the self-similarity of the multi-scale data of the spectral signal at a specified frequency was measured by fractal analysis, which was performed at every frequency in a frequency range of interest to acquire a fractal dimension curve. The fractal dimension curve reflected the self-similarity of the spectral signal at different scales, and the locations of local extremum of the curve were related to the position of the independent peaks. Finally, according to the fact and the feature parameters of the fractal dimension curve, independent peaks generated from mixed gas composition were separated from the spectral signal by an artificial neural network. The proposed algorithm in the paper carried on the fine analysis on the spectral signal at different scales using the multiresolution characteristic of the wavelet, and improved the analytical ability to parse the independent peaks with a high degree of overlap. The automatic measurement of the entire algorithm was realized using the artificial neural network. The validity of the proposed algorithm was verified by the analysis of experimental results, and the main factors that affected the algorithm were discussed.