The time-dependent formation of one-dimensional two-photon screening-photovoltaic (PV) grey spatial solitons under low-amplitude conditions is presented theoretically. The time-dependent propagation equation of two-photon screening-photovoltaic solitons is obtained by the numerical method. The results indicate that as the time evolves, the intensity width of grey screening-photovoltaic spatial solitons decreases monotonously to a minimum value towards the steady state. The higher the ratio of soliton peak intensity to the dark irradiation intensity, the narrower the width of grey solitons within the propagation time.