The kinetics model of Ar + 2 ionic excimer pumped by electron beam is built. The reactions on energy deposition of electron beam and formation of Ar + 2 ionic excimer are found. The reaction rate equations are given. The equations are calculated numerically and the relation between number density of Ar + 2 ionic excimer and time is obtained. With the calculation results of number density, the small signal gain is calculated. Experimental results are compared with the theoretical results. And it is proved that the 240 nm spectrum in the third continuum originates from the transition of Ar + 2 ionic excimer.