A 3-D DNS (Three-Dimensional Direct Numerical Simulation) study with detailed chemical kinetic mechanism of methane has been performed to investigate the characteristics of turbulent premixed oxy-fuel combustion in the condition relevant to Spark Ignition (SI) engines. First, 1-D (one-dimensional) laminar freely propagating premixed flame is examined to show a consistent combustion temperature for different dilution cases, such that 73% H2O and 66% CO2 dilution ratios are adopted in the following 3-D DNS cases. Four 3-D DNS cases with various turbulence intensities are conducted. It is found that dilution agents can reduce the overall flame temperature but with an enhancement of density weighted flame speed. CO2 dilution case shows the lowest flame speed both in turbulent and laminar cases. Reaction path analysis based on an in-house post-processing tool is performed to show that the chemical effect of dilution agent H2O leads to an increase of the key elementary reactions; however the total effect is endothermic compared with the counterparts for air condition case. This also results in a lower temperature of the oxy-fuel combustion. Furthermore, weak and strong levels of turbulent intensities 0.8 and 2.4 m/s are studied to show that the higher turbulent intensity leads to higher pressure rise rate, more flame surface wrinkling and higher displacement speed.