The GRACE (Gravity Recovery and Climate Experiment) satellite was launched in 2002 and great progress has been obtained in the Earth science and applications. The GRACE follow-on is a mission discussed broadly by the scientists and managers of space agencies all over the world to has an improved resolution of space and time for better geophysical applications. A program of Space Advance Gravity Measurement (SAGM) was arranged by the Strategic Priority Research Program on Space Science, the Chinese Academy of Sciences, and the idea of GRACE follow-on mission in China is discussed, including the mission goal, the research on Earth science and application, and the studies on critical technologies such as the inertial sensor, laser interferometer, micro propulsion, drag free technology, and satellite platform.