A series of Two-Dimensional Direct Numerical Simulation (2-D DNS) cases are performed to investigate the effects of CO2 and H2O on premixed turbulent oxy-fuel combustion (case oxy-H2O, case oxy-CO2) in a constant vessel. A DNS solver for low Mach reacting flow is developed based on open source code OpenFOAM. The chemical effects of CO2 and H2O are isolated by a pair of artificial species. 2-D DNS results shows the flame surface of oxy-CO2 case trends to be wrinkled with small convex and concave structures due to a lower laminar flame speed and a smaller effective Lewis number. Moreover, the response of flame surface to the curvature is different with corresponding dilute agent. Owing to the high binary diffusion coefficient between H2O and H, the negative curvature effect on fast diffusing species, e.g. H and H-2, are enhanced in oxy-H2O, and results in a higher burning velocity. The effects of CO2 on H transport are contrary to the effects of H2O and the oxidation process is slowed due to the elementary reaction CO2 + H double left right arrow CO + OH, which result in a more uniform Heat Release Rate (HRR) distribution on flame surface. In addition, chemical reaction pathway analysis is performed to elucidate the chemical effects of CO2 and H2O. It is found that CO2 and H2O will cool down the temperature of burnt region compared with N-2. Finally, an alternative solution is raised to counteract the negative effect of CO2 on flame speed, which should be useful in the development and design of oxy-fuel combustion.