An experimental system to measure the elastic wave velocities of hot-pressed polycrystalline samples at high pressure and high temperature has been installed at SPring-8. It uses a combination of the ultrasonic pulse-echo-overlap method and Kawai-type multi-anvil apparatus (SPEED-1500). X-ray radiographic imaging enables the sample length to be determined at high pressure and high temperature, which is indispensable for precise determination of elastic wave velocity. Precise measurements of the elastic wave velocities of various minerals have been determined at pressures up to 19 GPa and temperatures up to 1673 K. The experimental technique provides the precise elastic wave velocities of various materials corresponding to those in the Earth's mantle.