A graph with n vertices in which every pair of distinct vertices is connected by a unique edge is called a complete graph with n vertices, denoted by Kn. A graph with n vertices in which every vertex has degree 2 is called a cycle, denoted by Cn. Let {v1, v2, v3, v4, v5} be the vertex set of C5. If we add another five vertices w1, w2, w3, w4, w5 and five edges {vi, wi}, 1≦i≦5, then we call this graph a 5-sun graph, denoted by S(C5). Let G be a simple graph and G1,G2,…,Gt be subgraphs of G. If G1,G2,…,Gt satisfy the following conditions： (1) E(G1)∪E(G2)∪...∪E(Gt)= E(G) (2) ∀1≦i≠j≦t，E(Gi)∩E(Gj)= Ø , then we call G can be decomposed into G1, G2, …, Gt. If G1, G2, …, Gt are isomorphic to H, then we call G can be decomposed into H. In this thesis, we prove that： (1) if n≡1 (mod 20), then Kn can be decomposed into 5-sun graphs. (2) if n≡0 (mod 20), then Kn can be decomposed into 5-sun graphs. (3) if n≡5 (mod 20), then Kn can be decomposed into 5-sun graphs. (4) if n=16, 36, then Kn can be decomposed into 5-sun graphs.