By jointly solving two-centre material equations with a nonzero exteal electric field and coupled-wave equations,we have numerically studied the dependence of the non-volatile holographic recording in LiNbO3:Ce:Cu crystals on the exteal electric field. The dominative photovoltaic effect of the non-volatile holographic recording in doubly doped LiNbO3 crystals is directly verified. And an exteal electric field that is applied in the positive direction along the c-axis (or a large one in the negative direction of the c-axis) in the recording phase and another one that is applied in the negative direction of the c-axis in the fixing phase are both proved to benefit strong photorefractive performances.Experimental verifications are given with a small electric field applied exteally.