  If the c-quark has an anomalous color-electric dipole moment (CEDM), it may
serve as a new source of CP violation. The strength of such a CP violation
depends on the size of the CEDM, d'_c. We propose two effective ways of testing
it from the large sample of psi'->J/psi+pi(+)+pi(-) at the Beijing
Spectrometer, and the obtained result, |d'_c|<3X10^{-14} e cm (95% C.L.), gives
the first experimentally determined upper bound on the CEDM of the c quark.
