  The rebrightening phenomenon is an interesting feature in some X-ray,
optical, and radio afterglows of gamma-ray bursts (GRBs). Here, we propose a
possible energy-supply assumption to explain the rebrightenings of radio
afterglows, in which the central engine with multiple active phases can supply
at least two GRB pulses in a typical GRB duration time. Considering the case of
double pulses supplied by the central engine, the double pulses have separate
physical parameters, except for the number density of the surrounding
interstellar medium (ISM). Their independent radio afterglows are integrated by
the ground detectors to form the rebrightening phenomenon. In this work, we
firstly simulate diverse rebrightening light curves under consideration of
different and independent physical parameters. Using this assumption, we also
give our best fit to the radio afterglow of GRB 970508 at three frequencies of
1.43, 4.86, and 8.46 GHz. We suggest that the central engine may be active
continuously at a timescale longer than that of a typical GRB duration time as
many authors have suggested, and that it may supply enough energy to cause the
long-lasting rebrightenings observed in some GRB afterglows.
