Kink-like flapping motions of current sheets are commonly observed in the magnetotail. Such oscillations have periods of a few minutes down to a few seconds and they propagate toward the flanks of the plasma sheet. Here, we report a short-period (T approximate to 25 s) flapping event of a thin current sheet observed by the Magnetospheric Multiscale spacecraft in the dusk-side plasma sheet following a fast Earthward plasma flow. We characterize the flapping structure using the multi-spacecraft spatiotemporal derivative and timing methods, and we find that the wave-like structure is propagating along the average current direction with a phase velocity comparable to the ion velocity. We show that the wavelength of the oscillating current sheet scales with its thickness as expected for a drift-kink mode. The decoupling of the ion bulk motion from the electron bulk motion suggests that the current sheet is thin. We discuss the presence of the lower hybrid waves associated with gradients of density as a broadening process of the thin current sheet.