A theory of screening-photovoltaic solitons is improved in biased photorefractive-photovoltaic crystals. The self-deflection of screening-photovoltaic solitons arising from diffusion effects is investigated using perturbation analysis. It is concluded that are the center of the optical beam moves on a parabolic trajectory and the central spatial frequency component shifts linearly with the propagation distance. The self-deflection of screening-photovoltaic solitons can be controlled by changing the external voltage or by rotating the polarization of the light. When photovoltaic effect is neglectable, the nonlinear wave equation of screening-photovoltaic solitons is the nonlinear wave equation of screening solitons, and their self-deflection is the self-deflection of screening solitons. When the external electric field is absent, the nonlinear wave equation of screening-photovoltaic solitons is the nonlinear wave equation of photovoltaic solitons in the closed and the open circuit, and their self-deflection predict that photovoltaic solitons is of the self-deflection.