The runaway breakdown model induced by fast electrons is promising in explaining the nanosecond-pulse breakdown. In this paper, runaway process and collision ionization of fast electrons are discussed. Based on the relations between the electron energy and effective retarding force, the evolution of injected electron energy as a function of distance away from the avalanche head was simulated. The higher applied electric filed strength is, the lower the runaway energy threshold is and the more fast electrons can runaway, and gas pressures affect the runaway process of fast electrons greatly. Moreover, the runaway breakdown process under the high-voltage nanosecond pulse is described qualitatively.