In spectroscopy, the compositional analysis of the spectrum is important, such as extracting information about the species of spectral objects contributing to spectral data from an emission spectrum of photon energy. A quantitative spectral component analysis method based on Maximum Likelihood Estimation using Expectation Maximization (MLEM) is developed, which could quantitatively decompose out the components of the measured spectrum of low counts and surpass conventional techniques which belong to classification or regression. Abundant experimental and simulated spectra data on gamma-ray spectrum of radionuclides are presented to demonstrate and evaluate this method, while the ingredient radionuclides in the mixed spectrum are identified accurately with high precision. It will be a powerful and alternative method recommended for the circumstances needing fast and quantitative spectral analysis, including radionuclide identification (gamma-ray spectra), biomass or mineral composition (near-infrared spectra), laser-induced breakdown spectra and other spectroscopy scenarios.