The grain growth is very important because of its great influence on the various materials properties. Therefore, in this study, the effects of anisotropic grain boundary energy on grain growth in 2-D have been investigated with a large scale phase field simulation model on PC. A $2000{ imes}2000$ grid system and the initial number of grains of about 73,000 were used in the computer simulation. The anisotropic ratio of grain boundary energy, ${sigma}_{max}/{sigma}_{min}$, has been varied from 1 to 3. As the anisotropy increased, the grain growth exponent, n, increased from 2.05 to 2.37. The grain size distribution showed a central plateau in the isotropic case, and was changed into no central plateau and the increasing population of very small grains in the anisotropic case, resulting from slowly disappearing grains. Finally, simulated microstructures were compared according to anisotropy.