The Agulhas Current (AC) is one of the strongest western boundary currents in the world, which plays an important role in global climate change. To study on its variability of strength, the velocity of the current core observed from satellite altimeters, a representative indicator of AC strength, is used to define an Extreme Acceleration Event. There are 28 events from January 1993 to May 2020, lasting for 291 days in total, and the mean velocity is up to 1.58 m/s. During the events, anticyclonic eddies occur in the offshore flank of AC, which can be traced to the Mozambique Channel and south of Madagascar. It is the anticyclones from upstream areas that interact with AC through shearing leading to the increase of AC core velocities. In addition to the anticyclones, AC moves offshore during the events, performing as cyclonic anomalies in the inshore flank. An Offshore Movement Index shows the strongest offshore displacements appear before the events about 5 days. Moreover, the temperature and salinity vertical structures of AC change when the events happen, inducing the isopycnal surfaces to incline.