A 3D DNS (Three-dimensional direct numerical simulation) study with detailed chemical kinetic mechanism of methane has been performed to investigate the characteristic of turbulent premixed oxy-fuel combustion relevant to traditional spark ignition (SI) engine conditions. H2O and CO2 are adopted as the dilution agents in oxy-fuel combustion. In order to keep a consistent temperature profile compared with those of air-fired cases, 73% and 66% of H2O and CO2 in oxidizer by volume ratio are used. At first, laminar premixed flames are conducted to study the effect of the dilution molar fraction on the process of flame propagation. It is found that decreasing the dilution molar fraction will increase the flame propagation speed in both H2O and CO2 dilution cases, and there exists a temperature limitation because of chemical equilibrium. Reaction path analysis is performed to show that the chemical effect of dilution agent CO2 leads to a lower volume averaged temperature in the final stage of combustion compared with zero dilution cases due to the decomposition of CO2 through the reaction of CO2+H=CO+OH. The same phenomenon is observed in H2O dilution case. Furthermore, weak, medium and strong levels of turbulent intensities 0.8, 1.6 and 2.4 m/s are investigated to show that the turbulent intensity has a positive effect on the formation of CO and C2H2 by turbulence/chemistry interactions. Increasing turbulence leads to more wrinkling and the intensification of elementary reactions and therefore the increment of the flame displacement speed. It also implies that for oxy-fuel combustion, an appropriate turbulent intensity is good for emissions while maintains a suitable temperature profiles.