Given two connected graphs, G and H. The Order and size of Gand H, are u and v, and m and n, respectively. Graph G square edge-corona H, denoted by G ⋄2 H and defined as G ⋄2 H: = (G ⋄ H) ⋄ H, that is a graph obtained from G, the first v-copies of H that is Hh , with h ∈ {1,2,…, v], and the second v(1 + 2n + m)-copies of H that is Hhk , with h ∈ {1,2,…, v] and k ∈ {1,2,…,1 + 2n + m] and joining the terminal vertices of eh ∈ E(G), with eh = ihjh and ih , jh ∈ V(G), to all vertices of Hh , and then joining the terminal vertices of ek = rksk , ek ∈ G ⋄ H, to all vertices of Hhk . In this paper, the spectrum of the adjacency, Laplacian, and signless-Laplacian matrices of the graph G ⋄2 H will be analyzed further.