According to the band transport model theory, we establish the temporal evolution for dynamic equations concerning screening photovoltaic solitons in LiNbO3 crystal in this paper. By using the finite difference method, we find that there exist large self-deflection bright and dark screening photovoltaic solitons in LiNbO3 crystal, where the shape of the solitons becomes asymmetry ic with the increase of time. In addition, the absolute value of slope of the curve in deflection direction turns larger, while it tends to be smaller in the opposite direction as time increases. On the other hand, analysis shows that the factors related to the degree of self-deflection and deformation include acceptor concentration NA, dark radiation Id and applied electric field E0. When NA rises, the self-deflection degree and the deformation of bright soliton become smaller and the counterpart of dark soliton has opposite tendency while Id and E0 keep invariant. Moreover, for the bright and dark solitons, the space charge field induced in crystals is easier to reach saturation as Id diminishes and there is no saturation phenomenon in both cases when the ratio between center light intensity and dark radiation intensity is 10-1. With the E0 increases, the bright soliton self-deflection degree and deformation decrease, while the dark soliton self-deflection degree and deformation increase.