This paper study the non-synchronous vibration (NSV) of a high speed multistage axial compressor using rigid blade and vibrating blade with fluid-structural interaction(FSI). The unsteady Reynolds-averaged Navier-Stokes (URANS) equations and mode based structural dynamic equations are solved. A low diffusion E-CUSP Reimann solver with a 3rd orderWENO scheme for the inviscid fluxes and a 2nd order central differencing for the viscous terms are employed. A 1/7th annulus sector of IGV-rotor-stator is used with a time shifted phase lag BC at circumferential boundaries. An interpolation sliding boundary condition is used for the rotorstator interaction. The URANS simulation for rigid blades shows that the leading edge(LE) tornado vortices, roughly above 80% rotor span, travel backwards relative to the rotor rotation and cause an excitation with the frequency agreeing with the measured NSV frequency. The predicted excitation frequency of the traveling vortices in the rigid blade simulation is a non-engine order frequency of 2603 Hz, which agrees very well with the NSV rig testing. For the FSI simulation, the results show that there exist two dominant frequencies in the spectrum of the blade vibration. The lower dominant frequency is close to the first bending mode. The higher dominant frequency close to the first torsional mode agrees very well with the measured NSV frequency . The simulation conducted in this paper appears to indicate that the NSV is excited by the traveling vortex.