A free piston double diaphragm shock tube was newly developed for generation of high Mach number shock wave. Its characteristics was investigated for various operation parameters; such as a strength of the diaphragm at the end of the comparession tube, an initial pressure of low pressure tube, an initial pressure of medium pressure tube and the volume of compression tube. Under the restriction of fixed pressures for the driver high pressure tube (32×10^5Pa) and the low pressure tube (40Pa) in which the high Mach number shock wave is generated, a velocity of 12.2km/s was attained for the shock wave generated in an air of the low pressure tube.