Raman spectroscopy, with its unique "molecular fingerprint" characteristics, is an essential tool for label-free, non-invasive biochemical analysis of cells. It provides precise information on cellular biochemical components, such as proteins, lipids, and nucleic acids by analyzing molecular vibrational modes. However, overlapping Raman spectral signals make spectral unmixing crucial for accurate quantification. Traditional unmixing methods face challenges: unsupervised algorithms yield poorly interpretable results, while supervised methods like BCA rely heavily on accurate reference spectra and are sensitive to environmental changes (e.g., pH, temperature, excitation wavelength), causing spectral distortion and reducing quantitative reliability. This study addresses these challenges by introducing a parameterized Voigt function into the linear spectral mixing model for element spectrum compensation, using iterative least-squares optimization for adaptive unmixing and quantitative analysis. Simulations show that the Voigt-compensated unmixing algorithm improves spectral fitting accuracy and robustness. Applied to Raman spectra from Hela cell apoptosis and iPSCs differentiation, the algorithm accurately tracks biochemical molecular changes, proving its applicability in cellular Raman spectral analysis and a precise, reliable, and versatile tool for quantitative biochemical analysis.