The characteristics of spray, auto-ignition, and the combustion process of di-methyl ether (DME) were investigated using a 3-D simulation of a combustion vessel under various engine conditions, including high temperature and pressure. Spray impingement and non-premixed combustion models were incorporated into the computational fluid dynamics code, called STAR-CD. A Peng-Robinson equation of state was introduced to calculate the evaporation rate of DME droplets that were exposed to high-pressure conditions. A Laminar flamelet concept was used to simulate non-premixed combustion. A skeletal chemical kinetics mechanism consisting of 28 species and 45 reactions was used as the chemical mechanism for DME. Compared with the experimental data, the flamelet concept combustion model predicted the essential features of the combustion process and auto-ignition characteristics of the DME spray reasonably well for various initial conditions. The combustion process of a direct injection engine fueled by DME was also simulated and verified through experimental data.