The temporal evolution and morphology of grain growth in three dimensions were simulated by Monte Carlo method. In order to prevent impingement of grains of like orientation, new algorithm was adopted. The anisotropy of the grain boundary energy is incorporated into the model. Compared with the case in which no anisotropy of boundary energy is assumed, the suppression of grain growth was observed at the initial stage of growth in the grain structure with anisotropic grain boundary energy. However, the growth rate is higher at the later stage. The grain size and the face number distributions become broad. To evaluate the profile of the grain size distribution, a parameter called microstructural entropy, S, is defined. It was shown that the characteristics of size distribution profile may be represented by the value S. The average size of n-faced grain is proportional to the grain face number, n. The effect of the anisotropy of grain boundary energy on the n-dependence of the average grain size is not evident. The nearest neighbour face number correlation similar to the Aboav-Weaire relation in two dimension is observed in both grain structures with isotropic grain boundary energy and anisotropic grain boundary energy.