Effect of anisotropy in grain boundary energy on kinetics of grain growth and topological properties of grain structure in two dimensions was simulated by the phase field model. Misorientation distribution in a system with anisotropic grain boundary energy is found to be time-dependent. Fraction of low angle grains boundaries increases with time and high angle grains disappear fast. The average area is found to be proportional to time in both isotropic and anisotropic cases. The anisotropy in grain boundary energy delays the growth rate. The scaled grain size and the edge number distributions become time-independent in both isotropic and anisotropic cases. Anisotropy in grain boundary energy broadens the scaled grain size and the edge number distributions. The characteristics of the size distribution can be represented by the variation in a parameter, called microstructural entropy. The nearest neighbor face correlations obtained by the simulated grain structures with isotropic and anisotropic grain boundary energies are quite similar to the Aboav–Weaire relation.