Compound grey number and its grey degree are of importance for research on grey number and it algorithm rules. This paper proposes definitions of compound grey number and corresponding grey degree based on the "field" and axiomatic definition of grey degree, formulizes the grey degree of compound grey number by giving full consideration to the variations of "field" when compound grey number is generated from simple grey numbers, thus enrich the original definition of grey degree. Furthermore, this paper investigates the linear convergence of grey degree of compound grey number. Examples show the plausibility of these definitions and linear convergence, and the validity of Accumulated Generating Operation in terms of excluding outside disturbance.
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