The non-Fourier effects on transient thermal response in semitransparent medium with black boundary surfaces caused by a periodic irradiation are studied. The processes of the transient coupled radiative-conductive heat transfer in a one-dimensional semitransparent slab with black boundaries are analyzed numerically. The hyperbolic heat conduction equation is solved by the flux-splitting method, and the radiative transfer equation is solved by the discrete ordinate method. The transient thermal responses obtained from hyperbolic heat conduction equation are compared with those obtained from the classical parabolic heat conduction equation. The results show that the non-Fourier effect can be important when the conduction-to-radiation parameter and the thermal relaxation time of heat conduction are larger. The non-Fourier effect can be important even at a long time after the initial transient if the periodic irradiation at boundary is oscillatory with the period of oscillation of the same order of magnitude as the thermal relaxation time of conduction.