A fiber Bragg grating (FBG) sensor with an unbalanced Mach-Zehnder fiber interferometer for the shock stress measurement is proposed and demonstrated. An analysis relationship between the shock stress and the central reflection wavelength shift of the FBG is firstly derived. In this sensor, the optical path difference of the unbalanced Mach-Zehnder fiber interferometer is ~3.1 mm and the length of the FBG is 2 mm. An arctangent function reduction method, which can avoid sine function's insensitive zone where the shock stress measurement has a reduced accuracy, is presented. A shock stress measurement of water driven by one stage gun (up to 1.4 GPa), with good theoretical accuracy (~10%), is launched.