Oxygen combustion of CH4-CO2 mixture in a small-scale counterflow burner was studied. A diffusion flame was stabilized in the gap between opposed ports ejecting fuel and oxygen gases, and its thickness which depended on the gap distance between burner ports, inner diameter of burner tubes, flow rate of gases and fuel gas component was measured. The gas flow rates were varied such that the apparent equivalence ratio became constant at unity, while the gap distance was varied in the range from 1 mm to less. It was shown that the flame thickness decreased monotonically as the gap distance decreased and that the diffusion flame became thinner when the methane concentration in fuel gas became lower. Increased flame thickness was observed at large gas flow rate, and a diffusion flame was found in smaller gap distance at larger inner diameter. From these data, the relation between the flame thickness and the flame stretch rate was summarized, showing that the flame thickness decreased as the flame stretch became stronger, i.e. the thickness varied inversely with the square root of stretch rate. To elucidate the dependence of the flame thickness on the flame stretch rate, the flame thickness normalized by the average velocity of oxygen gas and the inner diameter was introduced. It was confirmed that the normalized flame thickness depended only on the flame stretch rate.