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The occurrence of earthquakes is closely related to the crustal geotectonic movement and the migration of mass, which consequently cause changes in gravity. The Gravity Recovery And Climate Experiment (GRACE) satellite data can be used to detect gravity changes associated with large earthquakes. However, previous GRACE satellite-based seismic gravity-change studies have focused more on coseismic gravity changes than on preseismic gravity changes. Moreover, the noise of the north–south stripe in GRACE data is difficult to eliminate, thereby resulting in the loss of some gravity information related to tectonic activities. To explore the preseismic gravity anomalies in a more refined way, we first propose a method of characterizing gravity variation based on the maximum shear strain of gravity, inspired by the concept of crustal strain. The offset index method is then adopted to describe the gravity anomalies, and the spatial and temporal characteristics of gravity anomalies before earthquakes are analyzed at the scales of the fault zone and plate, respectively. In this work, experiments are carried out on the Tibetan Plateau and its surrounding areas, and the following findings are obtained: First, from the observation scale of the fault zone, we detect the occurrence of large-area gravity anomalies near the epicenter, oftentimes about half a year before an earthquake, and these anomalies were distributed along the fault zone. Second, from the observation scale of the plate, we find that when an earthquake occurred on the Tibetan Plateau, a large number of gravity anomalies also occurred at the boundary of the Tibetan Plateau and the Indian Plate. Moreover, the aforementioned experiments confirm that the proposed method can successfully capture the preseismic gravity anomalies of large earthquakes with a magnitude of less than 8, which suggests a new idea for the application of gravity satellite data to earthquake research.