The adsorption of CO, CO2, CH4, H2, N2 and N2O on armchair (5,5) boron nitride nanotube (BNNT) with and without the doping of transition metals (TM), i.e. Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu or Zn, was investigated using the density functional theory calculation. The results indicate all the considered gases are physically adsorbed by weak interaction on the pure BNNT, revealing that pure BNNT has poor sensing performance for these gases. TM are then doped in the B or N vacancy of BNNT to improve the sensitivity and selectivity. As a result, it was found that the gas adsorption performance of BNNT is obviously enhanced due to the introduction of TM dopant atom. In particularly, according to the results of adsorption energy, Cu doped BNNT (Cu-BNNT) system shows a high selectivity toward CO molecule compared with other metal doped systems. This is further confirmed by the density of state, energy gap and charge transfer analyses. Furthermore, based on the sensor performance analysis, it was found that Cu-BNNT also has favorable desorption characteristics for CO. Therefore, this study concluded that Cu-BNNT can be used as a superior sensor material with high sensitivity, selectivity and favorable recycle time for CO gas.