In this presentation, a novel phase field grain growth model combined with a micro-elasticity effect including elastic anisotropy and inhomogeity is presented to demonstrate the effect of micro-elasticity on grain growth and texture evolution. We report on texture evolution and abnormal grain growth induced by external elastic load from the viewpoint of micro-elasticity and first demonstrate that the previous mechanism (macroscopic viewpoint) on the effect of external elastic load on grain growth does not work in strain-controlled system. In contrast to the macro-elastic descriptions, strong localization of strain energy density and inhomogeneous distribution even inside grains are observed. Moreover, elastically soft grains with a higher strain energy density grow at the expense of the elastically hard grains to reduce the total strain energy. It is observed that strong <100>//ND fiber texture was developed in poly-crystalline Cu with initial random texture by biaxial external strain while <111>//ND fiber texture evolved in biaxial external stress condition. Even, grain growth of <100>//ND textured grains is occurred as abnormal grain growth when <100>//ND textured grains are surrounded by <111>//ND fiber textured grains.