  Extended high-energy(>100MeV) gamma-ray emission that lasts much longer than
the prompt sub-MeV emission has been detected from quite a few gamma-ray bursts
(GRBs) by Fermi Large Area Telescope (LAT) recently. A plausible scenario is
that this emission is the afterglow synchrotron emission produced by electrons
accelerated in the forward shocks. In this scenario, the electrons that produce
synchrotron high-energy emission also undergo inverse-Compton (IC) loss and the
IC scattering with the synchrotron photons should be in the Klein-Nishina
regime. Here we study effects of the Klein-Nishina scattering on the
high-energy synchrotron afterglow emission. We find that, at early times the
Klein-Nishina suppression effect on those electrons that produce the
high-energy emission is usually strong and therefore their inverse-Compton loss
is small with a Compton parameter Y < a few for a wide range of parameter
space. This leads to a relatively bright synchrotron afterglow at high energies
that can be detected by Fermi LAT. As the Klein-Nishina suppression effect
weakens with time, the inverse-Compton loss increases and could dominate over
the synchrotron loss in some parameter space. This will lead to a faster
temporal decay of the high-energy synchrotron emission than what is predicted
by the standard synchrotron model, which may explain the observed rapid decay
of the early high-energy gamma-ray emission in GRB090510 and GRB090902B.
