We investigate a scheme for making leptogenesis by means of the $CP$ violating decays of the seesaw Majorana neutrinos proposed by Fukugita and Yanagida. However, in order to avoid the wash-out of the produced lepton number we propose the production of the Majorana neutrinos to occur non-thermally and sufficiently late. After this time, in consequence, the B-L (baryon minus lepton) quantum number becomes a good ``accidental symmetry'' protecting the asymmetry produced. This non-thermal leptogenesis at late time is realized by a boson decaying into the Majorana neutrinos with a long lifetime. Suggestively this boson could correspond to a scalar field which causes the cosmic inflation, the inflaton, and thus its decay means really the reheating of the Universe. We find that this mechanism works well even if the lightest Majorana neutrinos are not produced sufficiently or not present, and the decays of the heavier seesaw Majorana neutrinos can be responsible to the baryon asymmetry in the present Universe, as we illustrate by the example of the family replicated gauge group model.