Based on Pomeron exchange model, elastic production of vector meson in electro-proton interaction is investigated with both linear and non-linear Pomeron trajectory. A numerical calculation for J/ψ production is performed. The effect of the energy scale so and photon virtuality Q2 on differential cross section are also predicted. Agood agreement with experimental data is obtained. Our conclusions are that the Pomeron exchange model is a successful description of J/ψ electro-production, the dependence of the differential cross sections on Q2 is negligible, the linear trajectory is a good approximation to non-linearity of the Pomeron trajectory, and the value of the energy scale parameter so is dependent on the momentum transfer, namely its effect is moderate at low momentum transfer but it causes no difference at high momentum transfer | t |≥ 1.25 GeV2.