We calculated, from first principles, the Landau frequency λ to investigate the effects of spin fluctuation on the magnetic damping of Fe and Ni metals as well as L10-type ordered alloys, namely, FePt, CoPt, FePd, and MnAl, assuming random arrangements of spins as an effect of thermal activation through coherent potential approximation and the tight-binding linear muffin-tin orbital method. The results show that the λ of these systems are similar to conductivity in the weak spin fluctuation region and resistivity in the strong fluctuation region as well as in the lattice vibration system. Qualitatively, this behavior is consistent with the experimental results for temperature dependence of the λ of Fe and Ni metals. For L10-type alloys, the magnitude of the magnetic damping is in the following (decreasing) order: CoPt, FePt, FePd, and MnAl.