Abstract: A sharp-interface method combined with a low-dissipation weighted essential non-oscillatory (WENO) scheme was introduced to simulate the compressible Kelvin-Helmholtz instability. As the material interface was described as a contact discontinuity, this method resolved the exact tangential velocity discontinuity. By normalizing the original smoothness indicators with that of the optimal stencil, a modified WENO method with low dissipation was developed. While still keeping good shock-capturing properties, the modified method decreases the over damping in moderate flow field considerably, and is able to achieve comparable accuracy as that of hybrid methods. Different from previous simulations with single fluid or miscible interface methods, which suppress the high-wave-number modes by initially prescribed finite-width shear layer or fast numerical dissipation, this method allows the development of high-wave-number perturbation. However, the simulations still suggest that the high-wave-number perturbation show different behavior from previous simulations and linear theory on ideal Kelvin-Helmholtz instability but resemble those on shear layer with finite thickness.