Flutter is a self-sustained vibration which could create serious damage to compressor blades. Improving the efficiency and accuracy of Fluid-Structure Interaction (FSI) method is crucial to flutter analysis. An efficient FSI method which combines a fast mesh deformation technology and Double-Passage Shape Correction (DPSC) method is proposed to predict blades flutter under traveling wave modes. Firstly, regarding the fluid domain as a pseudo elastic solid, the flow mesh deformation and blade vibration response can be quickly obtained by solving the governing equations of the holistic system composed of blade and pseudo elastic solid. Then, by storing and updating the Fourier coefficients on the circumferential boundary, the phase-lagged boundary condition is introduced into the computational domain. Finally, the aerodynamic stability for the blades of an axial compressor under various Inter-Blade Phase Angle (IBPA) is analyzed. The results show that the proposed method can effectively predict the characteristics of aerodynamic damping, aerodynamic force and blade displacement. And a conceptual model is proposed to describe the motion behavior of the shock wave. Compared with the multi-passage method, the proposed method obtains almost the same unstable IBPA interval and the blade displacement error is less than 3.4%. But the calculation time is significantly shortened especially in small IBPA cases.