A new algorithm is proposed to deconvolve the infrared spectrum of complex hydrocarbon mixtures in the 3000-2800 cm^-1 region. The algorithm enables the accurate estimation of the contribution of methyl and methylene groups in petroleum samples, which is highly characteristic for their composition. The algorithm is developed based on the analysis of FT-IR spectra of seventy oil fractions, practically covering the whole range of a petroleum refinery intermediate and final products. The experimentally derived spectra are deconvolved by fitting three Lorentzian and one asymmetric Gaussian distributions, corresponding to methyl and methylene asymmetric and symmetric stretching vibrations. Molar absorptivities for these peaks are estimated from the FT-IR spectra of pure n-alkanes and alkyl-aromatics. The curve fitting procedure is implemented in Sequential Quadratic Programming (SQP) utilizing linear and non-linear constraints to incorporate chemical information, including the absorbance band positions and their molar absorptivity values. The developed methodology manages to reconstruct efficiently the FT-IR spectra of petroleum fractions, as indicated by the Mean Square Error (MSE) metric. The correctness of the selected peaks (position, amplitude) is further demonstrated by the practically constant ratios of the peak areas obtained for the asymmetric and symmetric methyl and methylene absorption bands, respectively of the whole data set. The algorithm facilitates the spectra modeling and the accurate estimation of the fitted methyl and methylene peak areas, which can be used for calculating specific compositional parameters of oil samples instead of the usually employed peak heights. Such modeling is extremely important for heavy petroleum fractions, where detailed compositional information is difficult to be obtained.