An implicit Large Eddy Simulation code for compressible flows have been developed, based on the idea of Monotonically Integrated LES. We employ Weighted Compact Nonlinear Scheme in order to attain high accurate resolution of the flowfield. The developed code is verified for the two-dimensional homogeneous turbulent flow, by comparing the inertial range of the energy spectrum with the Direct Numerical Simulation. The comparisons with other two LES approaches are also made. It is shown that the present approach can reproduce the inertial range in the energy spectrum comparable to that by the DNS. A truncation of energy spectrum occurs naturally at high wave number limit, which indicates that the dissipative effect is included properly in the present approach. The present approach can capture the vorticity contours very sharply without any numerical oscillations.