Hydrogen-dimethy ether(DME) partially premixed compression ignition(PCCI) engine combustion was investigated in a single cylinder compression ignition engine. Hydrogen and DME were used as low carbon alternative fuels to reduce green house gases and pollutant. Hydrogen was injected at the intake manifold with an injection pressure of 0.5 MPa at fixed injection timing, $-210^{circ}CA$ aTDC. DME was injected directly into the cylinder through the common-rail injection system at injection pressure of 30 MPa. DME inejction timing was varied to find the optimum PCCI combustion to reduce CO, HC and NOx emissions. When DME was injected early, CO and HC emissions were high while NOx emission was low. As the DME injection was retarded, the CO and HC emissions were decreased due to high combustion efficiency. NOx emissions were increased due to the high in-cylinder temperature. When DME were injected at $-30^{circ}CA$ aTDC, reduction of HC, CO and NOx emissions was possible with high value of IMEP.