Grain growth of a single-phase material with Read–Shockley anisotropic grain boundary energy was simulated using a modified Monte Carlo (MC) algorithm in which the local system energy is minimized in every step. The microstructure evolution in the presence of anisotropy is reproduced correctly. Providing that the initial grain orientations are distributed randomly, the parabolic growth law is not affected by the degree of anisotropy, which in turn affects the grain growth rate only. These findings are supported by three arguments rooted in previous theoretical and simulation results.