  We show that the twist-2 light-cone wave-functions of eta_c and J/\psi can be
factorized with nonrelativistic QCD(NRQCD) at one-loop level, where the
nonperturbative effects are represented by NRQCD matrix elements. The
factorization is achieved by expanding the small velocity v, which the c- or
\bar c- quark moves inside a rest quarkonium with. At leading order of v the
twist-2 light-cone wave-functions of eta_c and J/\psi can be factorized as the
product of a perturbative function and a NRQCD matrix element. The perturbative
function is calculated at one-loop level and free from any soft divergence. Our
results can be used for the production of J/\psi\eta_c through e^+e^-
-annihilation and of a charmonium in B-decays, which are studied in experiment
of two B-factories.
