Large-eddy simulations of an ideally expanded supersonic jet at Mach number 1.8 are performed by a high-order unstructured grid solver for aiming at the validation for aero-acoustic applications. The developed solver is based on the flux reconstruction scheme to discretize unstructured hexahedral grids. The localized artificial diffusivity scheme is employed to capture shock waves robustly and to retain high-order accuracy away from the shocks. The turbulent jet flow is obtained by the FR-LAD solver using the degree of polynomial up to p=4. The computed results are in reasonable agreement with the experimental and numerical data in the literatures for time-averaged and fluctuating quantities.