A kinetic model, based on the "mobile proton" model of peptide fragmentation, was developed to quantitatively simulate the low-energy collision-induced dissociation (CID) spectra of peptides dissociated in a quadrupole ion trap mass spectrometer. The model includes most fragmentation pathways described in the literature, plus some additional pathways based on the author's observations. The model was trained by optimizing parameters within the model for predictions of CID spectra of known peptides. A best set of parameters was optimized to obtain best match between the simulated spectra and the experimental spectra in a training data set. The performance of the mathematical model and the associated optimized parameter set used in the CID spectra simulation was evaluated by generating predictions for a large number of known peptides, which were not included in the training data set. It was shown that the model is able to predict peptide CID spectra with reasonable accuracy in fragment ion intensities for both singly and doubly charged peptide parent ions up to 2000 u in mass. The optimized parameter set was evaluated to gain insight into the collision-induced peptide fragmentation process.