  We investigate the leptogenesis via decays of heavy Majorana neutrinos which
are produced non-thermally in inflaton decays. We make a comprehensive study on
the leptogenesis assuming various supersymmetric (SUSY) models for hybrid, new
and topological inflations. For an estimation of the lepton asymmetry we adopt
the Froggatt-Nielsen mechanism for mass matrices of quarks and leptons. We find
that all of these models are successful to produce the lepton asymmetry enough
to explain the baryon number in the present universe. Here we impose low
reheating temperatures such as $T_R \lesssim 10^8$ GeV in order to suppress the
abundance of gravitinos not to conflict with the big-bang nucleosynthesis.
Furthermore, we find that the leptogenesis works very well even with $T_R
\simeq 10^{6}$ GeV in the SUSY hybrid or new inflation model. It is known that
such a reheating temperature is low enough to suppress the abundance of
gravitinos of mass $m_{3/2} \simeq 100$ GeV--1 TeV. Thus, the leptogenesis is
fully consistent with the big-bang nucleosynthesis in a wide region of the
gravitino mass.
