The largest Lyapunov exponents of the pressure signal between the stages of the eight-stage axial compressor of a certain engine is researched. It is presented that, taking zero of the largest Lyapunov exponent as the criterion of the stall of the compressor, the stage whose largest Lyapunov exponent first reaches zero is the stage of the first stall. Computational results demonstrate that the method can detect stall inception signal of compressor 0.2s before the start of deep rotating stall, and the third stage is the stage of the first stall.