  $J/\psi$ suppression in p-A collisions is studied by considering the nuclear
effects on parton distribution, energy loss of beam proton and the finial state
energy loss of color octet $c\overline{c}$. The leading-order computations for
$J/\psi$ production cross-section ratios $R_{W/Be}(x_{F})$ are presented and
compared with the selected E866 experimental data with the $c\overline{c}$
remaining colored on its entire path in the medium. It is shown that the
combination of the different nuclear effects accounts quite well for the
observed $J/\psi$ suppression in the experimental data. It is found that the
$J/\psi$ suppression on $R_{W/Be}(x_{F})$ from the initial state nuclear
effects is more important than that induced by the energy loss of color octet
$c\overline{c}$ in the large $x_F$ region. Whether the $c\overline{c}$ pair
energy loss is linear or quadratic with the path length is not determined. The
obtained $c\overline{c}$ pair energy loss per unit path length
$\alpha=2.78\pm0.81$ GeV/fm, which indicates that the heavy quark in cold
nuclear matter can lose more energy compared to the outgoing light quark.
