A theoretical model is proposed for the abnormal grain growth in thin films of columnar grains. In addition to the grain boundary energy usually considered for the grain growth in bulk materials, the influences of surface energy, interface energy and strain energy are also considered in the model. A reviewed analysis is given out for the anisotropy of energy. For fcc and bcc metal films, surface energy minimization generally favours (111) and (110) textures, while strain energy minimization generally favours (110) and (100) textures.