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The present work proposes a phase-field approach to realistically simulate abnormal grain growth in polycrystalline ceramic fibers at temperatures above 1000 °C. Under these conditions, grain growth is characterized by the formation of large elongated rectangular grains in a matrix of normal grains. The multi-phase-field model is extended by mechanisms which are responsible for the abnormal anisotropic growth: anisotropic interface energy, anisotropic interface mobility and a recrystallization driving force. Two types of mobility anisotropy are considered: anisotropy due to the misorientation between grains and anisotropy due to the dependency on inclination angles. The experimental data from heat treatments of the ceramic fiber Nextel 610 at 1200–1300 °C with different dwell times are examined by the proposed model. The comparison of the experiment and the simulation results at various times shows that the extended multi-phase-field model is able to simulate the microstructure realistically. In most model cases, abnormal grains have a rectangular shape, similar to the experiment. The best fit of the experimental grain size distribution and the grain shape is achieved by the simulation with the misorientation dependency of the interface mobility. Furthermore, it was shown that a strong decrease on the grain growth rate with time, observed in the experiment, can be reproduced by the simulations taking into account the segregation of impurities on grain boundaries that results in the decreasing grain boundary mobility.