Composting has been demonstrated to be effective in degrading organic pollutants (OP) whose behaviour depends on the composting conditions, the microbial populations activated and interactions with organic matters. The fate of OP during composting involves complex mechanisms and models can be helpful tools for educational and scientific purposes, as well as for industrialists who want to optimise the composting process for OP elimination. A COP-Compost model, which couples an organic carbon (OC) module and an organic pollutant (OP) module and which simulates the changes of organic matter, organic pollutants and the microbial activities during the composting process, has been proposed and calibrated for a first set of OP in a previous study. The objectives of the present work were (1) to introduce the COP-Compost model from its convenient interface to a potential panel of users, (2) to show the variety of OP that could be simulated, including the possibility of choosing between degradation through co-metabolism or specific metabolism and (3) to show the effect of the initial characteristics of organic matter quality and its microbial biomass on the simulated results of the OP dynamic. In the model, we assumed that the pollutants can be adsorbed on organic matter according to the biochemical quality of the OC and that the microorganisms can degrade the pollutants at the same time as they degrade OC (by co-metabolism). A composting experiment describing two different 14C-labelled organic pollutants, simazine and pyrene, were chosen from the literature because the four OP fractions simulated in the model were measured during the study (the mineralised, soluble, sorbed and non-extractable fractions). Except for the mineralised fraction of simazine, a good agreement was achieved between the simulated and experimental results describing the evolution of the different organic fractions. For simazine, a specific biomass had to be added. To assess the relative importance of organic matter dynamics on the organic pollutants’ behaviour, a sensitivity analysis was conducted. The sensitivity analysis demonstrated that the parameters associated with organic matter dynamics and its initial microbial biomass greatly influenced the evolution of all the OP fractions, although the initial biochemical quality of the OC did not have a significant impact on the OP evolution