The H-join graph is obtained on the basis of disjoint graphs G₁,G₂,…,G_k and by joining each vertex of G_i to each vertex of G_j whenever i is adjacent to j in H.In particular,the P₂-join graphs {G₁,G₂} is the ordinary join graph G₁∨G₂.The Laplacian characteristic polynomial of the H-join graph was studied,and the relations between the Laplacian spectrum of the H-join graph and those of the graphs G_i(i=1,2,…,k) and H were obtained,especially for the K_k-join graph and K_s,t-join graph.Moreover,the fact was proven that the H-join of Laplacian integral graphs {G₁,G₂,…,G_k} is also Laplacian integral when H is the complete graph,the complete bipartite graph or the graph of order not greater than 4 except for P₄.