  We investigate the effects of the convection in the hyperaccretion disk
around a stellar-mass black hole, which is considered to be the central engine
of gamma-ray bursts (GRBs), with simple analytical calculations. If the
convective energy transfer in the vertical direction becomes efficient compared
with the inward advective energy transport, the hyperaccretion disk is expected
to be hotter and the neutrino emission due to the electron-positron
annihilation becomes the most efficient cooling process. We find that the
sequence of the thermal equilibrium solutions for the convective hyperaccretion
disk would have a viscously unstable branch, especially when the viscosity
parameter is relatively small (alpha <~ 0.01). This means that the sporadic
mass accretion onto a black hole would occur in this disk. We propose that this
process can be the origin of the highly variable lightcurves observed in the
prompt emissions of GRBs.
