DME (Di-Methyl Ether) is synthetic product that is produced through dehydration of methanol or a direct synthesis from syngas. And it is able to save fossil fuel and reduce pollutants of emission such as PM and $CO_2$. In spite of its advantages it is difficult to design DME fuelled engine system because DME fuel may cause to severely generate cavitation and corrosion in fuel delivery system due to physical properties of DME. Therefore, in this study three-dimensional internal flow characteristics with consideration of cavitation were predicted in the DME injector using diesel and DME fuel. Moving grid technique was employed to describe needle motion and 1-D hydraulic simulation of injector was also simulated to obtain transient needle motion profiles. The results of simulation show that cavitations was generated at the inlet of nozzle near high velocity region both diesel and DME. And mass flow rate of DME is reduced by 4.73% compared to that of diesel at maximum valve lift because cavitation region of DME is much more larger. To increase flow rate of DME injector, internal flow simulation has been conducted to investigate the nozzle hole inner R-cut effect. The flow rates of diesel and DME increase as R-cut increases, and flow coefficient of DME fuel injector was increased by 6.3% on average compared with diesel fuelled injector. Finally, optimum shape of DME injector nozzle is suggested through the comparison of flow coefficient with variation of nozzle hole inner R-cut.