Rotating stall limits the stable operating range of compressors， and a deep understanding and accurate prediction of this phenomenon is key to stall prediction and control. Existing models for stall prediction are based on simplification of the compressor geometry and flow， and thus applications of these models to stall onset prediction of actual compressors are faced with considerable challenges. Meanwhile， despite the progress in experimental measurements and flow simulations， most experiments and numerical simulations are phenomenological research， and did not reveal the root cause of compressor flow instability. Moreover， due to the complexity of three-dimensional flow measurements and the high cost of unsteady simulations， most stall studies are conducted only under isolated working conditions of a particular compressor， as a systematic parametric study to identify the key influencing factors is too costly. In order to circumvent the shortcomings of both measurements and unsteady simulations， a global stability analysis method based on the efficient eigenvalue solution of the three-dimensional flow governing equation is proposed. This method can obtain not only the spatial resolution that is difficult to achieve by experimental measurement， but also the same rich information of the three-dimensional flow perturbation development at a cost two to three orders smaller than the unsteady simulation. In this paper， for a typical transonic compressor annular cascade， the computational cost of the proposed method is only 28% of that for computing one steady speedline， and 155 times faster than the unsteady calculation. Therefore， the proposed method provides an important research tool for accurate and rapid prediction and mechanism research of rotational stall of compressors.