A mathematical and physical model of electron-gas collisions is constructed. The experimental observation and theoretical analysis demonstrate that light emissions of a carbon nanotube-field emission display (CNT-FED) at different vacuum levels are mainly caused by electron bombardment on the phosphor. Light emission of the phosphor, excited by ultraviolet (UV) light derived from gas discharge, is not found even if the vacuum level is very poor. If vacuum level is too poor, a large amount of gas ionization will reduce the electric potential difference between the cathode and anode, so electrons are not emitted. The numerical calculations for the mean frequency of electron-gas collision indicate that the product of gas pressure and distance between the electrodes (pd) is a better parameter to characterize the effect of vacuum level for FED than gas pressure only, and when the distance between the cathode and anode is increased, the vacuum level must be improved to obtain the same effect.