The present research work has been carried out to study the flame structure of nitrogen-diluted methane flames in a laminar non-premixed oxygen-enhanced co-flow configuration system. A wide range of experiments are performed using nitrogen as a diluent with methane in jet for oxygen percentage variation in co-flow with two different burners of 4 and 9-mm diameter. The fuel stream is modeled by mixing methane and nitrogen gases. The oxidizer is modeled by mixing oxygen and nitrogen gases where the oxygen concentration level is varied from 100 % to blow-off. The fuel compositions diluted with nitrogen is varied from 12-100 % of methane and jet flow rate is maintained at 0.5 liter per minute (LPM) throughout all experiments. The co-flow rate is kept at 10 LPM for all the cases. A high co-flow rate makes the flame more stable, and it may sustain till a higher fuel dilution level. The flame length is measured under the influence of oxygen enrichment level. From experimental studies, it is found that the flame length for both 4-mm and 9-mm burner is highly sensitive to change in oxygen percentage in the oxidizer stream.