  We study a leptogenesis scenario in which the heavy Majorana neutrinos are
produced non-thermally in inflaton decays in the supersymmetric economical
SU(3)_C X SU(3)_L X U(1)_X model with inflationary scenario, and for this
purpose neutrino masses play the key role. Due to the inflaton with mass in the
GUT scale, the model under consideration provides successful neutrino masses,
which is different from ones without inflationary scenario. The
lepton-number-violating interactions among the inflaton and right-handed
neutrinos appear at the one-loop level, and this is a reason for non-thermal
leptogenesis scenario. The bound followed from the gravitino abundance and the
cosmological constraint on neutrino mass/the neutrino oscillation data is m_\nu
3 \simeq \frac{0.05}{\delta_{eff}} eV. By taking the reheating temperature as
low as T_R= 10^6 GeV, we get a limit on the ratio of masses of the light
heavies neutrino to those of the inflaton to be \fr{M_{R1}}{M_{\phi}} = 0.87.
