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We calculate the exclusive charmonium photo-production in the framework of color glass condensate.To obtain a good description of the vector meson production experimental data at HERA,we introduce a vector meson mass dependent skewness factor into the skewness effect.Then we extend the skewness improved model to the LHC energies.The numerical results of our model are in good agreement with the J/ψ and ψ(2S) data in ultraperipheral proton-proton collisions at LHC,which show the significance of the vector meson mass-dependent skewness factor.A prediction of the exclusive charmonium photo-production in ultra-peripheral nucleus nucleus collisions is performed since it can provide a good way to test the effectiveness of the color glass condensate.