In this paper, the combustion characteristics of Diesel and biodiesel fuels are investigated and compared. Based on the experimental data obtained from a medium-duty Diesel engine, a multi-phase combustion model, which is applicable to both Diesel and biodiesel fuels, is developed and it shows satisfactory accuracy within the test range in this study. A preliminary ignition-delay correlation is established by considering not only the in-cylinder physical factors such as pressure and temperature, but also the fuel property variations. It is also capable of modeling the premixed and mixing-controlled combustion by using two cascaded Wiebe functions. Through a grey-box parameter identification approach, a set of Wiebe coefficients, which are partially physics-based, are found; then the model can have a reasonable accuracy for the range of experiments conducted. Based on the multi-phase model, prediction can be made for the CA50 (crank angle for 50% heat release), which is very important for combustion timing feedback control. (C) 2013 Elsevier Ltd. All rights reserved.