Earthquakes are among the major natural disasters facing the world.Earthquakes can threaten safety of people and cause serious damage to property and the economy of a region.Our country is one nation that has had serious earthquake disasters throughout history，with 4 400 large earthquakes being recorded.Seismic intensity is 7 degrees or higher for 60 % of the nation’s land，with 50% of the cities and 67% of the big cities located in these high（i.e.，≥ 7） intensity areas.Therefore，having the ability to predict earthquakes would help to reduce the risk posed to people and human made structures.This article examines the gravity anomaly，one of the earthquake forerunners，and the relation between gravity anomalies and earthquakes.This study is based on the concept that when tectonic movement occurs，the earth’s crust extrudes or extends in every direction. As a result，gravity will be in a state of imbalance and under the action of an equilibrium force，the earth’s crust will restore to a balanced stable condition.During this adjustment，the gravity field will adjust and change until balance is restored.A formula is used to briefly describe the three influencing factors that affected the gravity anomaly：the density changes，movement of the outer fluid，and changes of measurement elevation.In the second part of the study，gravity variation diagrams are drawn with respect to time and space before the earthquake of Yushu，Tangshan and Wenchuan.It can be seen from the cases that the gravity anomaly before earthquakes is obvious：gravity changes constantly near the epicenter，and the gravity gradient is higher than usual.There are strong tectonic activities during earthquake gestation.Large deformations are produced in the fault zones and the weak areas of the earth’s crust，thus forming some crustal thickness difference and density difference，and the phenomena of gravity anomalies are shown.In this part，the causes of the gravity anomaly are also conjectured：tectonic movement and the invasion of subsurface fluid. Finally，two prediction methods of gravity are introduced：mobile gravity observation and GRACE gravity observation.The gravity changes because of crustal deformation and material changes in the fault zones，which result from crustal movement during earthquake gestation.We believe that evolution characteristics of the gravitational field can help us to explain current tectonic activity.The whole process from gestation to eruption of the mid-strong earthquake can be tied to gravity anomaly，thus providing reliable basis for earthquake prediction.Through the study of the gravity anomaly，the characteristics and change can be understood including the quality and density of underground medium，change of elastic modulus of the crust，and relationships between gravity anomalies and earthquakes.The related indicators of the short to medium term earthquake prediction in mobile gravity observation are summarized，and the case of Wenchuan earthquake is used to summarize the method of long term earthquake prediction using the GRACE satellite observation.