The electrical charging process in which uncharged aerosol particles are mixed with various concentrations of bipolar ion was studied by solving the basic equation, the so-called birth-death equation, numerically for various conditions. Some of the calculated results were compared with the experimental results obtained by the visible experimental technique. As a result, the time-dependent change in charge distribution of aerosol particles was found to be very rapid, and the equilibrium charge, which was effected by the ratio of number concentration of ion pairs to that of aerosols, was evaluated. The critical ratio where Boltzmann''s equilibrium distribution was attained was also evaluated.