  Considering the constraints from the experimental data on $\mu\rightarrow
e\gamma$, $\mu\rightarrow3e$, $\mu-e$ conversion etc., we analyze the Lepton
Flavor Violating decays $\phi(J/\Psi,\Upsilon(1S)) \rightarrow
e^+\mu^-(\mu^+\tau^-)$ in the scenarios of the minimal supersymmetric
extensions of Standard Model with seesaw Mechanism. Numerically, there is
parameter space that the LFV processes of
$J/\Psi(\Upsilon)\rightarrow\mu^+\tau^-$ can reach the upper experimental
bounds, meanwhile the theoretical predictions on $\mu\rightarrow e\gamma$,
$\mu\rightarrow3e$, $\mu-e$ conversion satisfy the present experimental bounds.
For searching of new physics, Lepton Flavor Violating processes
$J/\Psi(\Upsilon)\rightarrow\mu^+\tau^-$ may be more promising and effective
channels.
