In this paper, the effects of grain orientation on preferred abnormal grain growth in metallic films with hcp ((c/a)<1.633) structure have been analyzed with respect to strain energy. The calculated results showed that the lower strain energy densities were corresponding to those grains with lower l and higher equaled h and k plane oriented parallel to the plane of the film surface. It was predicted that, from strain energy minimization solely, the preferred orientations or textures in metallic films with hcp ((c=/a<1:633) structure, such as in a-Ti, a-Zr, a-Hf, Y and Rn, should be with lower l and higher equaled h and k.