In this paper non-synchronous vibration (NSV) of a GE axial compressor is simulated using a fully coupled fluid/strcuture interaction (FSI). Time accurate Navier- Stokes equations are solved with a system of 5 decoupled structure modal equations in a fully coupled manner. A 3rd order WENO scheme for the inviscid flux and a 2nd or- der central differencing for the viscous terms are used to resolve nonlinear interaction between vibrating blades and fluid flow. 1=7th annulus is used with a time shifted phase- lag (TSPL) boundary condition to reduce computational ef- forts. A fully conservative rotor/stator sliding boundary con- dition is employed to accurately capture unsteady wake prop- agation between the rotor and stator blades. The predicted dominant frequencies using the blade tip response signals are not harmonic to the engine order, which is the NSV. The blade vibration is torsionally coupled with highly oscillating blade pressure and is not damped out during the NSV. No resonance to the blade natural frequencies is found. The in- stability of tornado vortices in the vicinity of the rotor tip due to the strong interaction of incoming flow, tip vortex and tip leakage flow is the main cause of the NSV observed in this study.