An ignition and combustion model has been constructed for DI-PCCI combustion employing a stochastic turbulent mixing model with a reduced chemical kinetic scheme. The presented chemical kinetic model reproduced ignition delays and temperature histories of homogeneous mixtures predicted by a detailed reaction model. In PCCI combustion under constant volume condition, calculated heat release rate histories coincide with experimental results including the effects of injection conditions. From the analysis of relationship between equivalence ratio and temperature in mixture, the reason for delayed ignition due to enhanced fuel-air mixing was clarified.