  GRB 120326A is an unusual gamma-ray burst (GRB) which has a quite long
plateau and a very late rebrightening both in X-ray and optical bands. The
similar behavior of the optical and X-ray light curves suggests that they maybe
have a common origin. The long plateau starts from several hundred seconds and
ends at tens of thousands seconds. The peak time of the late rebrightening is
about 30000 s. We analyze the energy injection model by means of numerical and
analytical solutions, considering both the wind environment and ISM environment
for GRB afterglows. We especially study the influence of the injection starting
time, ending time, stellar wind density (or density of the circumburst
environment), and injection luminosity on the shape of the afterglow light
curves, respectively. We find that the light curve is largely affected by the
parameters in the wind model. There is a "bump" at the late time only in the
wind model too. In the wind case, it is interesting that the longer the energy
injected, the more obvious the rebrightening will be. We also find the peak
time of bump is determined by the stellar wind density. We use the late
continuous injection model to interpret the unusual afterglow of GRB 120326A.
The model can well fit the observational data, however, we find that the time
scale of the injection must be larger than ten thousands seconds. This implies
that the time scale of the central engine activity must be more than ten
thousands seconds. This can give useful constraints on the central engine of
GRBs. We consider a new born millisecond pulsar with strong magnetic field as
the central engine. On the other hand, our results suggest that the circumburst
environment of GRB 120326A is very likely a stellar wind.
