We have developed a phase-field model which can simulate the growth process of self-assembled SiGe/Si islands during deposition. The novel feature of this model is that it can reproduce the morphological transitions of islands, i.e., from single-faceted pyramid to multifaceted dome and from dome to barn, by taking a high anisotropy and a sixteen-fold anisotropy of surface energy into account. Two-dimensional simulations have been performed on a large computational model. As a result, island nucleation on the surface of a wetting layer, island morphological change and Ostwald ripening due to an interaction between two neighbor islands were well reproduced. The bimodal distribution of island size, which is a very important phenomenon in self-assembled quantum dots, could also be generated. Furthermore, it has been clarified that the bimodal distributions are largely affected by island morphological change from pyramid to dome. Furthermore, in order to discuss the mechanism of island growth, a simulation of single-island growth has been conducted and the variations of island size and energies have been estimated in detail. As a result, it is concluded that the island morphological transitions occur so as to reduce the elastic strain energy.