During asphalt mixture compaction, loads in the material are mainly transferred through contact between the stones and the interaction between the stones and the binder. The behaviour of such materials is suitable to model using the Discrete Element Method (DEM). In this study, a new DEM modelling approach has been developed for studying the asphalt compaction process, incorporating contact and damage laws based on granular mechanics. In the simulations, aggregate fracture is handled by a recently developed method of incorporating particle fracture in DEM, based on previously performed fracture experiments on granite specimens. The binder phase is modelled by adding a viscoelastic film around each DEM particle. This surface layer has a thickness that obtains the correct volume of the binder phase and has mechanical properties representative for the binder at different temperatures. The ability of the model to capture the influence of mixture parameters on the compactability and the eventual stone damage during compaction is examined for the cases of compaction flow test and gyratory compaction. Explicitly, the influence of different aggregate gradations, mixture temperatures and binder properties are studied. The results show that the proposed DEM approach is able to capture qualitatively and quantitatively responses in both cases and also provide predictions of aggregate damage. One large benefit with the developed modelling approach is that the influence of different asphalt mixture parameters could be studied without re-calibration of model parameters. Furthermore, based on comparative DEM simulations, it is shown that the proposed approach provides more realistic force distribution networks in the material.