  In the standard scenario of the fireball model of gamma-ray bursts(GRBs), the
huge initial energy release produces a relativistic blast wave expanding into
the external medium and a reverse shock moving into and heating the fireball
ejecta. We calculate the high energy gamma-ray emission due to inverse Compton
scattering of the synchrotron photons from relativistic electrons in the
reverse shock. Under the favorable values of the physical parameters of the
GRBs and the interstellar medium, our result shows that during the prompt
phase, this emission dominates over the component from the forward shock at
high energy gamma-ray bands. This mechanism can excellently account for the
observations of the prompt high energy gamma-rays detected by EGRET, such as
from GRB930131.
