Abstract: The grain growth during the annealing process of pure copper with homogeneous and heterogeneous structure (gradient structure and bimodal structure) were simulated by the phase field model and the ideal grain growth model. The results show that the change of grain boundary energy barrier had little effect on the growth rate of grain with homogeneous structure. When the annealing time was longer than 600 s, the growth rate of homogeneous structural grains had a larger step change. For heterostructural grains, the greater the grain boundary energy barrier, the slower the grain growth. In the gradient structure, the growth rate of small grains was the fastest, followed by that of medium grains, and that of large grains was the slowest. The larger the grain size, the smaller the influence of the grain boundary energy barrier on the growth rate. In the bimodal structure, the grain boundary energy barrier had greater influence on the growth rate of coarse grains than the fine grains. The growth rate of fine grains significantly decreased and of coarse grains increased after increasing number of coarse grains.