Abstract: For analyzing the evolution process of grey information, this paper aims to establish a mathematical structure theory of grey information which is limited and insufficient. Firstly, grey space theory is built to describe the connotation and extension of grey information, proving that grey information during evolution satisfies the grey kernel attribute invariance and grey information measure non-increasing principles. Secondly, the dynamic evolution of grey information is calculated based on grey information measurement. Then, complete steps of the grey clustering method based on grey information evolution theory are given. Our method can be extended to a general uncertain system.