Abstract: A strong interaction between shock wave and leakage vortex,induced by an intensive inter-impact of rotating motion on abrupt anti-pressure gradient,makes their formations and strengths varied.The vortex breakdown deteriorates the stability and efficiency of compressor and fan.So a model of interaction between shock wave and leakage vortex is formulated.The solution of vortex core movement equations shows that the small initiative vortex core velocity and enhanced initiative vortex core pressure will induce the vortex instability.The high Mach number and circulation gradient outside the vortex core will result in breakdown of the vortex.The analysis of the factors leading to vortex breakdown serves as a foundation for its controlling.