Vibrationally excited molecular nitrogen N-2(*) plays an important role in the F region ionosphere by increasing the loss rate of the dominant ion O+, thereby reducing the electron concentration in the F region of the ionosphere. In this paper, we use a theoretical numerical ionospheric model to study the effect of N-2(*) on the ionosphere during four time periods, each including both geomagnetically quiet and storm disturbed periods, through considering and not considering the role of N-2(*) in the numerical ionospheric model. The four periods simulated are (1) June 11 similar to 15, 1990; (2) May 14 similar to 20, 1997; (3) May 1 similar to 10, 1998 and (4) April 6 similar to 10, 2000. By comparing the simulated results with the observational ones, it is shown that N-2(*) has a significant effect on the ionosphere during high solar activity years, while for the low solar activity years, the role played by N-2(*). is very limited, much less than that in high solar activity years. It is also shown that for the high solar activity years, when constructing an ionospheric physical model, one must take into account N-2(*) not only for the geomagnetically disturbed period but also for the quiet period. Moreover, it is found that the effect of N-2(*) on the ionospheric electron density distribution depends on the vibrational temperature T-v adopted. When taking the value of T-n as T-v (where T-n is the background neutral temperature) the simulated result, compared with the observation one, is not as good as that when T-v is calculated by the steady state analytical solution. Moreover, our simulation results show that, for high solar activity years, the effect of N-2(*) on the distribution of ionospheric electron concentration is to reduce the electron density for the height above 150km, while its effect on the electron density below 150km is very small. The F-2 layer peak height h(m)F(2) is not affected basically by N-2(*).