A theory is presented to investigate the existence of incoherently coupled bright-dark photovoltaic soliton pairs in an unbiased photovoltaic crystal with uniform illumination. It is found that with the same photovoltaic photorefractive effect, the two optical beams with the same polarization and wavelength but which are mutually incoherent can form incoherently coupled bright-dark photovoltaic soliton pairs. The expression forms of optical field and the full-width at half-maximum (FWHM) of the bright and dark components are deduced. Taking CuKNSBN for example, the variation relations between the intensity profile and FWHM and the soliton intensity is discussed. The investigation results show that when incoherently coupled bright-dark soliton pairs form, the FWHM of the dark soliton is smaller than that of the bright soliton. Therefore, it contributes little to the refractive-index change. The propagation properties are also investigated by numerical method. It is found that incoherently coupled bright-dark photovoltaic soliton pairs can propagate stably in photovoltaic crystals. When the dark soliton beam is absent, the bright soliton can still propagate in the crystal with breathing shape. When the bright soliton beam is absent, however, the dark soliton beam collapses quickly.