We report the excitation of the non-steady-state photoelectro-motive force in a monoclinic gallium oxide crystal. The crystal grown in an oxygen atmosphere is insulating and highly transparent for a visible light, nevertheless, the formation of dynamic space-charge gratings and observation of the photo-EMF signal is achieved under the laser illumination with wavelength λ = 532 nm. The induced ac current is studied for the cases of zero and non-zero external electric fields, which imply the non-resonant and resonant mechanisms of space-charge recording. The dependencies of the signal amplitude versus the frequency of phase modulation, light intensity, spatial frequency, light polarization and value of the external dc electric field are measured. The material demonstrates the anisotropy along the [100] and [010] directions, namely, there is a weak difference of the transport parameters and a pronounced polarization dependence of the signal. The photoconductivity and diffusion length of electrons are estimated for the chosen light wavelength.