In order to decrease CO2 emission, relieve the pressure of natural gas supply and promote the scale consumption of hydrogen energy, using natural gas mixed with hydrogen for combustion is considered to be one of the most promising ways. At present, the research on natural gas mixed with hydrogen is mainly focused on industry. In this work, the combustion characteristics of a burner for domestic use with natural gas mixed with hydrogen were studied. A two-dimensional axisymmetric model of the burner was developed with Fluent software coupled with GRI 2.11 chemical reaction mechanism file. The numerical model was verified by comparing the numerical simulation results with the reference experimental results. Furthermore, the effects of different amount of premix of fuel and air, and secondary air flow velocity on combustion temperature, main free radical content and combustion pollutants were analyzed. The results showed that with the amount of premix (primary air coefficient) increasing, the peak temperature increased greatly, NO peak mass fraction increased firstly and decreased, CO peak mass fraction increased gradually. As the secondary air velocity (excess air coefficient) increased, the temperature and pollutant content changed little. Compared with the effect of amount of premix, the effect of air velocity was almost negligible.