Lean premixed combustion is a well known method for low $NO_x$ gas turbine combustor. But lean combustion is usually accompanied by flame instability. To overcome this problem, the hydrogen ($H_2$) was added to main fuel methane to increase flammable limit. In this paper, the effects of hydrogen addition on lean premixed combustion of methane ($CH_4$) were investigated numerically. Results showed that the extinction stretch rate increases and the extinction temperature constant with relatively small amount of $H_2$ addition. The flame temperature and NO emission increase with $H_2$ addition at the same stretch rate and equivalence ratio but it could increase the range of lean extinction and extinction equivalence ratio limit. Eventually, the $H_2$ addition case showed almost same or lower NO emission than no addictive $CH_4$ case in the extinction condition.