We have been developing an experiment on laser-induced double-shock compression of diamond foils to a metallic phase by means of impedance-mismatching technique. We measured the reflectivity from the rear side of the diamond foil with a velocity interferometer system for any reflector. The measured reflectivity of the diamond clearly increased with the double compression. Independently measured from an optical pyrometer indicates that the compressed temperature of the diamond was approximately 7300 K, which is much lower than that of the single shock. The experimental results strongly suggest the phase transition from diamond to metallic carbon.