  The energy loss effect of incoming gluon from $J/\psi$ production in p-A (or
d-A) collisions is investigated by means of the E866, RHIC and LHC experimental
data. The gluon mean energy loss per unit path length $dE/dL = 2.18\pm0.14$
GeV/fm is extracted by fitting the E866 experimental data for $J/\psi$
production cross section ratios $R_{W(Fe)/Be}(x_{F})$. The obtained result
indicates that the incoming gluons lose more energy than the incident quarks.
  By comparing the theoretical results with E866, RHIC, and LHC experimental
data, it is found that the nuclear suppression due to the incident gluon
(quark) energy loss reduces (increases) with the increase of the kinematic
variable $x_{F}$ (or $y$). The energy loss effect of incoming gluon plays an
important role on the suppression of $J/\psi$ production in a wide energy range
from $\sqrt{s}=38.7$ GeV to $\sqrt{s}=5.0$ TeV, and the influence of incident
quark energy loss can be ignored for high energy(such as at RHIC and LHC
energy).
