Current sheets (CSs), long stretching structures of magnetic reconnection above solar flare loops, are usually observed to oscillate, their origins, however, are still puzzled at present. Based on a high-resolution 2.5-dimensional MHD simulation of magnetic reconnection, we explore the formation mechanism of the CS oscillations. We find that large-amplitude transverse waves are excited by the Kelvin-Helmholtz instability (KHI) at the highly turbulent cusp-shaped region. The perturbations propagate upward along the CS with a phase speed close to local Alfvén speed thus resulting in the CS oscillations we observe. Though the perturbations damp after propagating for a long distance, the CS oscillations are still detectable. In terms of detected CS oscillations, with a combination of differential emission measure technique, we propose a new method for measuring the magnetic field strength of the CSs and its distribution in height.