In this paper, a plate equation involving supercritical damping and a logarithmic source term is considered. It is evident that the energy of the solution exhibits exponential decay in the linear case, with polynomial decay occurring in the subcritical case. However, the estimation is complicated in the supercritical cases, due to the failure of the embedding inequality and the presence of the logarithmic source, conventional multiplier approaches are unsuccessful. Motivated by Haraux and Tebou, a priori estimate for the integral ∫ Ω | u | m d x is provided. Subsequently, by combining the Nehari functional estimates and applying a modified multiplier method, we establish the logarithmical decay of the energy.