The first-principles approach based on density functional theory (DFT) achieves substantial success in the vast field of condensed matter physics. However, the limitation of the de facto standard method of local density approximation or generalized gradient approximation is also revealed, especially in the localized electron system. The GW approach is one of the promising methods to overcome such problems. In this talk, I would like to review the quasiparticle self-consistent GW approach and introduce its application to the ferromagnetic shape memory alloy of Ni-Mn-Ga. Besides this, I would like to introduce the improvement of DFT by including the weak interaction of magnetic dipole-dipole, which is one of the origins of magnetic anisotropy.