In this paper, we introduce a geodesic metric space called generalized Cayley graph (gCay(P,S)) on a finitely generated polygroup.We define a hyperaction of polygroup on gCayley Belts graph and give some properties of this hyperaction.We show that gCayley graphs of a 151 polygroup by two different generators are quasi-isometric.Finally, we express a connection between finitely generated polygroups and geodesic metric spaces.