  We propose to test CP symmetry in the decay $\jp\to \gamma \phi\phi$, for
which large data sample exists at BESII, and a data sample of $10^{10}$
$J/\psi$'s will be collected with BESIII and CLEO-C program. We suggest some CP
asymmetries in this decay mode for CP test. Assuming that CP violation is
introduced by the electric- and chromo-dipole moment of charm quark, these CP
asymmetries can be predicted by using valence quark models. Our work shows a
possible way to get information about the electric- and chromo-dipole moment of
charm quark, which is little known. Our results show that with the current data
sample of $J/\psi$, electric- and chromo-dipole moment can be probed at order
of $10^{-14}e cm$. In the near future with a $10^{10}$ data sample, these
moments can be probed at order of $10^{-16}e cm$.
