We examined the characteristics of $NO_x$ emission for CH4/air non-premixed flames using the exhaust gas recirculation(EGR) methods, which are the air-induced EGR(AI-EGR) and fuel-induced EGR(FI-EGR) methods. Our experimental results show that the $NO_x$ emission index($EI_{NOx}$) decreased with increasing EGR ratio. In the range needed to form a stable flame, the reduction rate of $EI_{NOx}$ for the FI-EGR method was approximately 29% when the EGR ratio was 20%, and the reduction rate for the AI-EGR method was approximately 28% with 25% of the EGR ratio. According to the flame structure based on numerical results, high temperature regions for the FI-EGR method were narrower and lower than those for the AI-EGR method at the same EGR ratio. Furthermore, based on the experimental results for swirl flames, the reduction rate of $EI_{NOx}$ for the FI-EGR method was approximately 49% with 15% of the EGR ratio, while the maximum reduction rate for AI-EGR method was approximately 45% with 25% of the EGR ratio. Consequently, we verified that the FI-EGR method was more effective than the AI-EGR method in reducing $NO_x$ emission for non-premixed flames with EGR. We expect that the results of this study will provide fundamental information relating to hybrid combustion systems, which can be used in the design of combustion systems in the future.