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In this paper, the J/Ψ nuclear absorption effect is studied at RHIC and LHC energies with the EKS98 shadowing parameterizations. By assuming that the J/Ψ absorption cross section, σ_(abs), increases with the charmonium-nucleon (J/Ψ-N) center of mass energy, √(S_(J/ΨN)). it is found that σ_(abs) should depend on xf (or y) at a certain center of mass energy per nucleon pair, √(s), especially at LHC energies. The theoretical results with the x_F (or y)-dependence of the absorption effect are in good agreement with the experiment data from PHENIX in d-Au collisions and the predicted results will be examined by the forthcoming experimental data from LHC in d-Pb collisions. Finally, we also present baseline calculations of cold nuclear matter effects on J/Ψ production in nucleus-nucleus (A-A) collisions and find that the x_F (or y)-dependence of absorption effect is very small at both RHIC and LHC energies in A-A collisions.