The tip clearance effects on aero-elastic stability of axial compressor blades are investigated with two independent three-dimensional (3D) flutter prediction approaches: energy method and aero-elastic eigenvalue analysis. An axial compressor rotor which has encountered broken fault caused by flutter during the test rig and flight has been analyzed for five tip gap configurations. A consistent conclusion obtained by these two independent approaches shows the variation trend of aerodynamic damping is not monotonic, but aerodynamic damping at the least stable case shows a trend of first decrease and then increase with the rising of tip gap size, which is different from the results of other researchers and can be utilized to understand the conflict between the conclusions of different research work. Apart from the results of tip clearance effects on aero-elastic stability, the employed two methods have revealed the key factors involved in the flutter occurrence from a different perspective.