Abstract: High-precision acceleration measurement has a broad application prospect in the fields of inertial navigation and gravity field measurement. The acceleration measurement sensor based on cold atom interferometry can fully exploit the short wavelength, long evolution time, and precise frequency response of atomic matter waves, which is much higher than the measurement sensitivity, accuracy and long-term stability of traditional inertial sensors such as accelerometers and gravimeters, bringing significant changes to the existing acceleration measurement technology. Starting from the basic principle of cold-atom interferometric acceleration measurement, the research progress of cold-atom interferometric acceleration measurement technology at home and abroad over the past 30 years is reviewed. And at the same time, combining with the demand for acceleration measurement technology in the field of inertial navigation, it is analyzed and concluded that the development dynamics of cold-atom interferometric acceleration measurement technology and the key development direction are the integration and miniaturization of the system, the improvement of the repetition frequency and the measurement bandwidth, hybrid accelerometers and multi-axis acceleration measurement, etc. The aim is to improve and perfect the overall performance of cold-atom interferometric acceleration sensors, in order to boost and facilitate the advancement of cold-atom interferometric acceleration sensors to the stage of engineering applications, and to provide a powerful support to meet the strategic demand for high-precision inertial measurements from the national defense industry.