This paper proposes a new maximum likelihood approach for the deconvolution of identity and quantity of individual compounds based on the multicomponent mass spectra measured by mass spectrometry (MS). Mixture analysis of multicomponent mass spectra is, typically, based on a linear multicomponent mass spectrum model, where the compounds of the measured spectra to be solved are explicitly stated and assumed to be known. In many cases, however, the measured spectrum may contain unknown compounds that are not explicitly stated in the model and a commonly used least squares (LS) solution fails. Moreover, a standard improvement over the LS method in these cases, namely the M-estimation (ME) approach, also suffers from this same problem. Our method overcomes the limitations of the LS and ME methods by modeling the effect of the unknown compound(s) to the residual of the linear model. The experimental results presented show that this new approach can separate, more robustly, the complex multicomponent mass spectra into their individual constituents compared with the LS and ME methods.