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The non-thermal high-energy electron effects on Langmuir wave-particle interaction are investigated using an initial value approach. A Vlasov-Poisson simulation is employed based on the splitting scheme by Cheng and Knorr (1976). The kappa distribution function is taken as an example of non-thermal electrons. The modification is manifested as an increase in the Landau damping rate and a decrease in the real frequency for a long wavelength limit. A part of the analyses using the modified plasma dispersion function (Summers and Thorne 1991) is reproduced for £e = 2, 3 and 6. The dispersion relation from the initial value simulation and the plasma dispersion function compare favorably.(PACS numbers: 52.35.Fp, 52.35.Sb, 52.65.Ff).