Heavy quark production in high-energy nuclear p+A and D+A collisions has been a focus of interest for many years.The J/ψ suppression was proposed as a litmus test of the quark-gluon plasma(QGP) formation in the early days of relativistic heavy ion program. In order to study the impact of cold nuclear matter effects on J/ψ particle yields at high energy, we followed the DKLMT model which provided an improved analysis of the gluon saturation on the color singlet J/ψ production in d-Au collisions, we introduce the cold nuclear matter effects to the J/ψ production mechanism, and find the nuclear modification factor of the J/ψ at 200 GeV.The gluon saturation/CGC effect and the cold nuclear matter effect of dipole-nucleus interactions has been investigated by introducing a nuclear geometric effect function f(?) to study the nuclear geometry distribution effect in relativistic heavy-ion collisions. The geometry effect factor has been discussed and then we perform the numerical calculations of the corresponding nuclear modification factors(RdA) in rapidity and centrality. After let RdA compared to J/ψ experimental data at RHIC. It is found that the M-DKLMT model can well describe the J/ψ experimental results at both forward- and mid-rapidity regions in dAu collisions at RHIC.Three parameter of the anomalous dimension(IIM,KKT,DHJ) are introduced in this paper, after combine with QSXY-model, the J/ψ production distributions at small x ans low transverse momentum(p T) has been performed, It has a reference value for the anomalous dimensions of CGC research on the central rapidity of the LHC. |