  We calculate lepton flavor violating (LFV) Z decays Z \to {{e_i^\pm}}e_j^\mp
(i, j = e, \mu, \tau ; i\neq j) in the Zee model keeping in view the radiative
leptonic decays e_i\to e_j\gamma (i = \mu, \tau ; j = e, \mu ; i\neq j), \mu
decay and anomalous muon magnetic moment (\mu AMM). We investigate three
different cases of Zee f_{ij} coupling (A) f_{e\mu}^2 = f_{\mu\tau}^2= f_{\tau
e}^2, (B) f_{e\mu}^2 \gg f_{\tau e}^2 \gg f_{\mu\tau}^2, and (C) f_{\mu\tau}^2
\gg f_{e\mu}^2 \gg f_{\tau e}^2 subject to the neutrino phenomenology.
Interestingly, we find that, although the case (C) satisfies the large excess
value of \mu AMM, however, it is unable to explain the solar neutrino
experimental result, whereas the case (B) satisfies the bi-maximal neutrino
mixing scenario, but confronts with the result of \mu AMM experiment. We also
find that among all the three cases, only the case (C) gives rise to largest
contribution to the ratio B(Z\to e^\pm\tau^\mp)/B(Z\to \mu^\pm \mu^\mp) \simeq
{10}^{-8} which is still two order less than the accessible value to be probed
by the future linear colliders, whereas for the other two cases, this ratio is
too low to be observed even in the near future for all possible LFV Z decay
modes.
