The grey Shapley value is a solution concept in cooperative games where the coalitional values are interval grey numbers. Recently, much attention has been paid on this value in Operations Research models and methods. The purpose of this study is to characterize this value on cooperative grey games. The grey Shapley value is characterized by following some axioms. Our axioms are g-efficiency, g-triviality , g-coalitional strategic equivalence, and g-fair ranking. These axioms give us a new perspective on the characterization of this value. Finally, some examples and applications of cooperative grey games are also given. It is hoped that this study will inform readers for axiomatic characterization of this value.