Through first principles, we first demonstrated the structural and thermal stability of monolayer Mo2B by analyzing the results of phonon spectrum and ab initio molecular dynamics simulations. In addition, the adsorption energies for four kinds common noxious molecules NO, NO2, CO, CO2 are calculated with values of −2.978 eV, −2.838 eV, −1.914 eV and −0.586 eV, respectively. The relatively low adsorption energy for NO, NO2 means that Mo2B has a high selectivity for these molecules. The charge transfer number of NO, NO2, CO, and CO2 on monolayer Mo2B are 0.855 e, 1.189 e, 0.658 e, and 0.926 e. The CO2/Mo2B system has smallest adsorption energy and a relatively large charge transfer value, which suggests Mo2B may be used as a highly reversible and sensitive detector for CO2. More importantly, the recovery time for CO2/Mo2B system is only 10−4 s. The recovery time for the other three molecules is calculated to exceed 1010 s at room temperature which indicates irreversible detection of these molecules. These results could provide guidance for the achievement of high-performance gas sensitive materials.