  We present a concrete supersymmetric grand unified model based on the
Pati-Salam gauge group SU(4)_c x SU(2)_L x SU(2)_R and leading naturally to
smooth hybrid inflation, which avoids the cosmological disaster encountered in
the standard hybrid inflationary scenario from the overproduction of monopoles
at the end of inflation. Successful `reheating' which satisfies the gravitino
constraint takes place after the termination of inflation. Also, adequate
baryogenesis via a primordial leptogenesis occurs consistently with the solar
and atmospheric neutrino oscillation data as well as the SU(4)_c symmetry.
