Using first principle and based on the density functional theory, we have studied the effect of the single vacancy on the electronic properties of armchair graphene nanoribbons (AGNRs). Results show that the system is the most stable when the vacancy is at edge site. It is found that AGNRs always become metallic, regardless of the vacancy position. As the vacancy concentration decreases, the influence of the vacancy position on band structures becomes weaker and weaker. As the ribbon width increases, the particular value characterizing the strength of metallicity decreases in oscillation. Vacancy-induced semiconductor to metal transition in AGNRs provides the theoretical direction for the application of graphene in the electrionic devices.