We study the domain formation in the v=2/3 fractional quantum Hall systems basing on the density matrix renormalization group (DMRG) analysis. The ground-state energy and the pair correlation functions are calculated for various spin polarizations. The results confirm the domain formation in partially spin polarized states, but the presence of the domain wall increases the energy of partially spin polarized states and the ground state is either spin unpolarized state or fully spin polarized state depending on the Zeeman energy. We expect coupling with external degrees of freedom such as nuclear spins is important to reduce the energy of partially spin polarized state.