The effects of a co-flow of oxygen-enriched air on the characteristics of a laminar jet diffusion flame of methane are experimentally investigated using a coaxial burner positioned vertically. The volume content of oxygen varies from 21% (air) to 30%. Flame structure is observed through the heights of flame lift-off and flame length based on initial rates of CH4, air, and oxygen percentages. Stability diagrams showing the states of the flame and transitions between these states are drawn. The reduction of the lift-off height observed during the addition of oxygen is explained by the increase of the laminar flame speed and heat release due to a higher flame temperature.