We present calculations of spin wave dispersions for antiferromagnetic MnO, NiO and ferromagneticα-MnAs based on the recently developed quasiparticle self-consistentGW method(QSGW); we have alreadyshown that QSGW gave a good quasiparticle picture for MnO and NiO in comparison withoptical experiments. To obtain the spin wave dispersions, we have developeda method to calculate the transverse dynamical spin susceptibility in therandom-phase approximation. This is a general method applicable not only toQSGW, but also to any first-principle method which gives the non-interacting (one-body)Hamiltonian to represent quasiparticles, e.g. the Kohn–Sham Hamiltonian in the densityfunctional theory. In the method, we first calculate the non-interacting spin susceptibilityfrom the supplied non-interacting Hamiltonian; then we obtain the spin susceptibilitywhere the size of the effective interaction is determined so as to satisfy a sum rule. ForMnO and NiO, the obtained spin wave dispersions show good agreement with experiments,in contrast to the cases in the local density approximation (LDA) and in theLDA+U. These results support our claim that the independent-particle picture is powerful enough even formaterials like NiO and MnO classified to the Mott insulator, that is, the quasiparticle pictures byQSGW work well to describe their linear responses. Forα-MnAs, we find a collinear ferromagnetic ground state inQSGW, while this phase is unstable in the LDA.