  We present results for charmonium-nucleon potential $V_{c\bar{c}-N}(r)$ from
quenched lattice QCD, which is calculated from the equal-time Bethe-Salpeter
amplitude through the effective Schr\"odinger equation. Detail information of
the low-energy interaction between the nucleon and charmonia ($\eta_c$ and
$J/\psi$) is indispensable for exploring the formation of charmonium bound to
nuclei. Our simulations are performed at a lattice cutoff of $1/a\approx 2.1$
GeV in a spatial volume of $(3 fm)^3$ with the nonperturbatively $O(a)$
improved Wilson action for the light quarks and a relativistic heavy quark
action for the charm quark. We have found that the potential
$V_{c\bar{c}-N}(r)$ for either the $\eta_c$ and $J/\psi$ states is weakly
attractive at short distances and exponentially screened at large distances.
The spin averaged $J/\psi$-$N$ potential is slightly more attractive than that
of the $\eta_c$-$N$ case.
