Density functional theory (DFT) calculations have been employed to explore the adsorption properties of pristine and vacancy-defective AlN monolayer towards SO2 and NO2 in terms of their adsorption energies and electronic structures. The calculations with van der Waals effect are performed to study the binding mechanism of pristine and vacancy-defective AlN nanosheet with SO2 and NO2. Three types of vacancy defects are considered including Al-monovacancy, N-monovacancy and divacancy. The adsorption energies of vacancy-defective AlN monolayer towards SO2 and NO2 are found to be much higher than that of pristine nanosheet. The equilibrium adsorption sites and configurations of the gas molecules on AlN nanosheets are determined. The Bader charge transfer analysis reveals that a considerable amount of charge is transferred from the vacancy-defective AlN nanosheets to the gases leading to the increase of adsorption energies. The results of difference charge densities, band structures, electronic density of states and work function further give insight into adsorption energies. The dramatical changes of electronic band structures after gas interaction suggest the excellent adsorption properties of vacancy-defective AlN monolayer towards SO2 and NO2.