Abstract: G*-cone metric space is introduced for the first time. In this new cone metric space, a new set-valued compression mapping is studied. By constructing different iterative sequences, it is proved that the existence and uniqueness of common fixed point theorems for set-valued compression mapping in G*-cone metric spaces. This result enriches the fixed point theorem of set-valued compression in different metric spaces, and illustrates the applicability of set-valued compression in different metric spaces.