In this paper, the combination of conduction with radiation into a semitransparent medium which includes absorption, emission and scattering has been investigated. In order to Study the conduction in medium, the Non-Fourier heat conduction has been applied. In this model there is a time delay between heat flux and temperature gradient. Also, in contrast with Fourier heat conduction, the speed of heat propagation is finite. The radiation transfer equation has been solved via approximate method. Also to solve the energy conservation equation and Non-Fourier heat conduction simultaneously, flux-splitting method has been applied. The results show that the transient temperature responses are oscillatory for Non-Fourier heat conduction. Also the Non-Fourier effect can be important when the thermal relaxation time of heat conduction is large. In the initial times, the difference of transient temperature responses between the Fourier and the Non-Fourier heat conduction is large under this condition. For the laser-flash measurement of thermal diffusivity in semitransparent materials, omitting the Non-Fourier effect can result in significant errors.   Keywords: