The Weighted Compact Nonlinear Scheme (WCNS) developed by Deng et al. is applied to implicit LES of two-dimensional and three-dimensional homogeneous turbulent flowfield. Comparisons of the obtained energy spectrum with that given by Kawamura-Kuwahara scheme are made. It is shown that WCNS can reproduce inertial range in the energy spectrum fairly well for two-dimensional flowfield. A truncation of energy spectrum naturally occurs at high wave number limit with a favorable dissipative effect. Comparisons of the computed results with those given by Kawamura-Kuwahara scheme indicate that WCNS is more preferable to implicit LES in terms of numerical accuracy. However, for three-dimensional flowfield, the computed inertial range using WCNS is less obvious probably due to insufficient mesh resolution. In this study, we also consider a problem of two-dimensional inviscid double shear layer. This problem is solved by WCNS scheme for incompressible flow and also that for compressible flow. It is found that WCNS for compressible flow can reproduce the vorticity field of incompressible flow fairly well, though a slightly more dissipative nature is implied.