In columnar-grained film with anisotropy in the surface energy, abnormal grain growth occurs to minimize the overall energy. We studied the effect of grain boundary energy on the surface-energy driven abnormal grain growth in thin films using the Monte Carlo computer simulation. Our simulation results show that the growth speed of abnormal growth slows down when grain boundary energy increases. It is because the speed of normal growth driven by the grain boundary energy minimization gets faster with increasing grain boundary energy, while that of the abnormal growth induced by the fixed surface energy is consistent. The growth kinetics was monitored based on the growth velocity of the abnormal grains relative to the average growth velocity of all the grains. It was also found that the abnormal growth kinetics was retarded by impingements among abnormally growing grains when there was more than one abnormal grain.