  We investigate how the baryon asymmetry of our universe via leptogenesis can
be achieved within the framework of the seesaw model with Fritzsch type lepton
mass matrices proposed by Fukugita $et. al$. We study the cases with
CP-violating phases in charged lepton Yukawa matrix, however, with and without
Dirac neutrino Yukawa phases. We consider both flavor independent and flavor
dependent leptogenesis, and demonstrate how they lead to different amounts of
lepton asymmetries in detail. In particular, it is shown that flavor dependent
leptogenesis in this model can be worked out only when the CP phases in Dirac
neutrino Yukawa matrix become zero at the GUT scale. In addition to the CP
phases, for successful leptogenesis in the model it is required that the
degeneracy of the heavy Majorana neutrino mass spectrum should be broken and we
also show that the breakdown of the degeneracy can be radiatively induced.
