A (λKv, G)-design is a partition of the edges of λKv into subgraphs each of which is isomorphic to G. In this paper, we completely solve the case when G = G18 (G18 is notation from Bermond, Huang, Rosa and Sotteau, Ars Combin. 10 (1980), 211–254) and prove that the necessary condition λv(v− 1) ≡ 0 (mod 14) for the existence of a (λKv, G18)-design with any positive integer λ is also sufficient e...