Based on the generalized QCD vector meson dominance model, we study the electroproduction of a vector meson off a proton in the QCD inspired eikonalized model. Numerical calculations for the total cross section sigma(tot) and differential cross section d sigma/dt are performed for rho, omega and phi meson electroproduction in this paper. Since gluons interact among themselves (self-interaction), two gluons can form a glueball with quantum numbers I-G, J(PC) = 0(+), 2(++), decay width Gamma(t) approximate to 100 MeV, and mass of m(G)=2.23 GeV. The three gluons can form a three-gluon colorless bound state with charge conjugation quantum number C= -1, called the Odderon. The mediators of interactions between projectiles (the quark and antiquark pair fluctuated from the virtual photon) and the proton target (a three-quark system) are the tensor glueball and the Odderon. Our calculated results in the tensor glueball and Odderon exchange model fit to the existing data successfully, which evidently shows that our present QCD mechanism is a good description of meson electroproduction off a proton. It should be emphasized that our mechanism is different from the theoretical framework of Block et al. We also believe that the present study and its success are important for the investigation of other vector meson electro- and photoproduction at high energies, as well as for searching for new particles such as tensor glueballs and Odderons, which have been predicted by QCD and the color glass condensate model (CGC). Therefore, in return, it can test the validity of QCD and the CGC model.