We study a leptogenesis via decays of heavy Majorana neutrinos produced non-thermally in inflation decays. We find that this scenario is fully consistent with existing supersymmetric inflation models such as for topological or for hybrid inflation and the Froggatt-Nielsen mechanism generating hierarchies in quark and lepton mass matrices. The reheating temperature T-R of inflation may be taken as low as T-R similar or equal to 10(8) GeV to avoid the cosmological gravitino problem. (C) 1999 Published by Elsevier Science B.V. All rights reserved.