  We study CP violation in $J/\psi \rightarrow \Lambda \bar{\Lambda}$ decay.
This decay provides a good place to look for CP violation. Some observables are
very sensitive to the $\Lambda$ electric dipole moment $d_\Lambda$ and
therefore can be used to improve the experimental upper bound on $d_\Lambda$.
CP violations in the lepton pair decays of $J/\psi$ and $\Upsilon$ are also
discussed.
