  We investigate consequences of a continuously energy-injecting central engine
of gamma-ray burst (GRB) afterglow emission, assuming that a highly magnetized
pulsar is left beaming in the core of a GRB progenitor. Beaming and continuous
energy-injection are natural consequences of the pulsar origin of GRB
afterglows. Whereas previous studies have considered continuous
energy-injection from a new-born pulsar to interpret the deviation of afterglow
light curves of GRBs from those with the simple power law behavior, a beaming
effect, which is one of the most important aspects of pulsar emissions, is
ignored in earlier investigations. We explicitly include the beaming effect and
consider a change of the beaming with time due to a dynamical evolution of a
new-born pulsar. We show that the magnitude of the afterglow from this fireball
indeed first decreases with time, subsequently rises, and declines again. One
of the most peculiar optical afterglows light curve of GRB 970508 can be
accounted for by continuous energy injection with beaming due to a highly
magnetized new-born pulsar. We discuss implications on such observational
evidence for a pulsar.
