The kinetics and topology of grain growth in three dimensions were simulated using a phase-field model with anisotropic grain-boundary mobilities. In order to perform large scale calculations we applied both modifications of algorithms and parallel coding techniques to the Fan and Chen's phase-field algorithm. Kinetics of abnormal grain growth is presented. It is observed that the grains of a minor component which are at the beginning surrounded preferentially by boundaries of high mobility grow faster than the grains of a major component until the texture reverses completely. Additionally, topological results of grain structures, such as grain size distributions and grain face distributions, are discussed.