In this paper, an axiomatic system for the definition of degree of greyness of grey number is built based on discussion with two definitions of degree of greyness of grey number which have been put forward in the past. Taking axioms as the criterion for definition of degree of grayness of grey number, a new formula for definition of degree of grayness of grey number has been formed with measure of the right range of grey number and the background or field which is brought about by the grey number. The degree of uncertainty of grey number is described scientifically, and some problems present in old definitions have been surmounted in new definition.