A meso-scale jet flame model was established for the flame ports of domestic gas stoves. The influences of hydrogen addition ratio (β = 0%–25%) on the combustion limits were explored. The results show that with the increase of hydrogen addition ratio, the blow-off limit increases obviously, while the extinction limit decreases slightly, namely, the combustible range expands significantly. Quantitative analysis was carried out in terms of chemical effect and thermal effect. It was found that hydrogen addition will reduce O2 fraction in the pre-mixture for a constant equivalence ratio. Under near-extinction limit condition, since the flame is located at the nozzle exit, the external O2 cannot be entrained into or diffuse into the upstream of the flame, which leads to the decrease of reaction rate. However, for the near-blow-off cases, the external O2 can be entrained and diffuse into the flame, which compensates the difference of O2 content in the pre-mixture. Therefore, the combustion reaction is enhanced by hydrogen addition because more H radicals can be produced. In addition, as the flame is located closer to the tube with the increase of hydrogen addition ratio, heat transfer between flame and tube wall is augmented and the preheating of fresh mixture is strengthened by the inner tube wall. This heat recirculation effect becomes especially notable in low velocity cases. In conclusion, the extension of extinction limit by hydrogen addition is attributed to the thermal effect, while the increase of blow-off limit is mainly due to the intensification of chemical effect.