A performance of high-order Cellwise Relaxation Implicit Discontinuous Galerkin (DG-CRI) scheme on unsteady ow computation is investigated. The inviscid Taylor-Green vortex is first computed to demonstrate the capability of the high-order DG-CRI scheme on the homogeneous turbulence computation. The higher-order DG-CRI scheme gives better resolved small vortex structures, which is well indicated in the later decay of the kinetic energy and the higher enstrophy. In addition, the effects of the CFL number and the number of inner iterations are discussed by comparing with the results by explicit time integration. Then, the high-order DG method is applied for the LES computation of the turbulent channel ow, and the advantages of the high-order DG method in predicting accurate turbulent statistics are shown.