We calculate transverse spin susceptibility in the linear response method based on the ground states determined in the quasiparticle self-consistent GW (QSGW) method. Then we extract spin-wave (SW) dispersions from the susceptibility. We treat bcc Fe, hcp Co, fcc Ni, and B2-type FeCo. Because of the better description of the independent-particle picture in QSGW, calculated spin stiffness constants for Fe, Co, and Ni give much better agreement with experiments in QSGW than those in the local density approximation (LDA); the stiffness for Ni in LDA is two times greater than in experiment. For Co, both acoustic and optical branches of SWs agree with experiment. As for FeCo, we have some discrepancy between the spin stiffness in QSGW and that in experiment. We may need further theoretical and experimental investigations on the discrepancy.