According to recent studies, gas sensors based on MoSe2 have better detection performance than graphene-based sensors, especially for N-based gas molecules, but the reason for that is not fully understood at the microscopic level. Here, we investigate the adsorption of CO, CO2, NH3, NO and NO2 gas molecules on MoSe2 monolayer by the density functional theory calculations. Our results reveal that indeed MoSe2 monolayer is more sensitive to adsorption of N-containing gas molecules than C-containing, which can be attributed to the distinct charge transfer between the gas molecules and MoSe2. The conductance was further calculated using the nonequilibrium Green's function (NEGF) formalism. The reduced conductance was found for NH3 and NO2 adsorbed MoSe2, consistent with the high sensitivity of MoSe2 for NH3 and NO2 molecules in the recent experiments. In addition, the adsorption sensitivity can significantly be improved by an external electric field, which implies the controllable gas detection by MoSe2. The magnetic moments of adsorbed NO and NO2 molecules can also be effectively modulated by the field-sensitive charge transfer. Our results not only give microscopic explanations to the recent experiments, but also suggest using MoSe2 as a promising material for controlled gas sensing.