The occurrence of stall and surge in axial compressors has a great impact on the performance and reliability of aero-engines. Accurate and efficient prediction of the key features during these events has long been the focus of engine design processes. In this paper, a new body-force model that can capture the three-dimensional and unsteady features of stall and surge in compressors at a fraction of time required for URANS computations is proposed. To predict the rotating stall characteristics, the deviation of local airflow angle from the blade surface is calculated locally during the simulation. According to this local deviation, the computational domain is divided into stalled and forward flow regions, and the body-force field is updated accordingly; to predict the surge characteristics, the local airflow direction is used to divide the computational domain into reverse flow regions and forward flow regions. A single-stage axial compressor and a three-stage axial compressor are used to verify the proposed model. The results show that the method is capable of capturing stall and surge characteristics correctly. Compared to the traditional fully three-dimensional URANS method (fRANS), the simulation time for multi-stage axial compressors is reduced by 1 to 2 orders of magnitude.