This paper utilizes the Improved Delayed Detached Eddy Simulation (IDDES) to investigate the non-synchronous vibration (NSV) mechanism of a 1.5 stage high-speed axial compressor. The NSV occurs at a part speed in the rig test. A low diffusion E-CUSP approximate Riemann solver with a third order Weighted Essentially Non-Oscillating (WENO) scheme for the inviscid flux and a second order central differencing scheme for the viscous flux are employed to solve the 3D time accurate Navier-Stokes equations. The fully conservative sliding boundary condition is used to preserve the wake-propagation. The aerodynamic instability in the tip region induces two alternating low pressure regions near the leading and the trailing edge on the suction side of the rotor blade. It is observed that the circumferential tip vortex motion in the rotor passage above 75 % span and its coupling forces cause NSV at the operating speed. This instability moves in the counter-rotating direction in the rotational frame. The NSV results using URANS simulation is also presented for comparison. The predicted frequency with the IDDES and URANS using rigid blades agrees well with the measured frequency in the rig test. In addition to the NSV, the IDDES solver also captures the dominant engine order frequencies. The tip flow structures show the vortex filament with one end on the suction side of the rotor blade and other side terminating on the casing or the pressure side of the rotor blade.