As a reliable stall warning strategy, the fast wavelet method was introduced to successfully predict the aerodynamic instability of a multistage axial flow compressor. One single sensor installed at each stage is proved to be sufficient to predict the stability status in a three-stage axial flow compressor. The whole prediction strategy includes the dynamic pressure signal capture, disturbance extraction using decomposition and reconstruction via fast wavelet transform, and stall warning index calculation based on statistical probability distribution. On this premise, the first occurrence of the stall in this three-stage axial flow compressor is predicted to be within the first stage, which is consistent with the stall route captured by the eight transducers around the casing wall. Thereafter, the stall warning index is used to monitor the stability status during the continuous throttling process. Furthermore, the validation using tip air injection and inlet radial distortion indicated that the stall warning index decreases as the compressor's stability improves. Conversely, the deterioration of stability causes the increase of the stall warning index. Thus, experimental results demonstrate that the stall warning method based on fast wavelet analysis can predict the aerodynamic instability in actual application.