  It is well known that the Zee model induces small neutrino masses by
radiative corrections, where the bi-maximal flavor mixing is possible. We
analyze the cosmological condition in order for the baryon asymmetry generated
in the early universe not to be washed out in the
  Zee model. Since the lepton number is violated explicitly in the Zee model,
the baryon asymmetry might be washed out through the sphaleron processes
together with the lepton-number violating interactions. In this letter, we will
show that the baryon asymmetry is {\it not} washed out, although it has been
said that the Zee model cannot preserve the baryon asymmetry generated in the
early universe. This can be seen by considering an approximately conserved
number, $L' \equiv
  L_e-L_\mu-L_\tau$.
