Abstract: Let G be a graph and A an abelian group;Denote by F(G,A) the set of all functions from E(G) to A.Denote by D an orientation of E(G).For f∈F(G,A),an (A,f)-coloring of G under the orientation D is a function C:V(G)→A such that for every directed edge uv from u to v,c(u)-c(v)≠f(uv)．G is A-colorable under the orientation D, if for any function f∈F(G,A),G has an (A,f)-coloring. The group chromatic number χg(G) of a graph G is the minimum number m such that G is A-coloring for any Abelian group A of order ≥m under the orientation D. In this paper, the author discussed the group coloring of some kinds of double graphs based on the analysis of their traits. Let G be a path, we proved that the group chromatic mumber of double path is 3 and also proved the group chromatic number of double cycle is at most 5, among other things.