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The Landau damping of waves propagating in a plasma modeled by a Lorentzian (kappa) distri-bution with a spectral index · is investigated. In the high-frequency range, the dispersion relation of the electron Langmuir wave is obtained. The Landau damping rate equation is shown to have a thermal correction term that has not been found in previous studies. The dispersion relation of ion-acoustic waves is also investigated for the low-frequency range. Dampings of both the electron Langmuir and the ion-acoustic waves are suppressed as the spectral index · increases; i.e., the nonthermal e��ect decreases.