This paper conducts Delayed Detached Eddy Simulation(DDES) of a 3D wing flutter with free stream Mach number varied from subsonic to supersonic using a fully coupled fluid/structure interaction (FSI). Unsteady 3D compressible Navier-Stokes equations are solved with a system of 5 decoupled structure modal equations in a fully coupled manner. The low diffusion E-CUSP scheme with a 5th order WENO reconstruction for the inviscid flux and a set of 4th order central differencing for the viscous terms are used to accurately capture the shock wave/turbulent boundary layer interaction of the vibrating wing. The predicted flutter boundaries at different free stream Mach numbers achieve very good agreement with experiment. It appears that the transonic dip phenomenon is due to the anticlimax contribution of the second mode, which is caused by the complicated shock oscillation on the wing.