We developed a high fidelity spectral element solver for the simulation of the vortex induced vibration (VIV) a smooth cylinder at high Reynolds number (Re_D). The coordinate transformation method is employed to deal with the moving boundary due to the vibrating cylinder. The entropy viscosity method based on the residues of the vorticity transport equations is employed to deal with the turbulence colsure.  The solver is implemented on the spectral element code NekRS. With the solver, we have simulated VIV of a rigid cylinder in the Re_D range [10³, 10⁶], reduced order velocity (Ur) range [2,30]. In particular, for the cylinder only allowed to vibrate in crossflow only, in range 8×10⁴<Re_D<2.6×10⁵ and 8<Ur<25, large amplitude up to 2.3D is observed. To the best of our knowledge, it is first time that a numerical simulation is able to reproduce both the unusual large amplitude.