Abstract: By applying a new fitting parameter σJ/ψN ,weve calculated the differential cross section ratio R of J/ψ in high energy p-A and p-p collisions with three different nuclear medium effects.The plots of R vs.xF (y) calculated with selected nuclear effect models have been presented under E866,HERA,RHIC and LHC energy.By a comparison with the experimental data published recently,weve found that the results can reproduce the trend and magnitude of data,especially at the positive rapidity of RHIC and the negative of xF HERA.Our conclusion is helpful to identify the difference between the sign of quark-gluon formation and production suppression caused by cold nuclear effects,which is also an important test to the QCD matter in heavy ion collisions.