Accurate estimation of the Earth gravity field plays an important role in understanding the Earth geodynamic activities. After brief discussion on the objective of the gravity estimation, dedicated satellite missions for this purpose are described. Recently launched NASA/DLR Gravity Recovery and Climate Experiment (GRACE) mission, which consists of two co-orbiting low altitude satellites, is described. For the performance analysis, full numerical simulation was performed. The simulation procedure and its key instrument modelings are described. From the simulation results, a significant improvement on the Earth gravity field accuracy is expected.