The coarseness ξ(G) of a graph G is the maximum number of mutually line-disjoint nonplanar subgraphs of G. Clearly, ξ(G) = 1 if and only if G is nonplanar and G has no two line-disjoint subgraphs homeomorphic to K3,3 or K5. In this paper, we obtain a necessary and sufficient condition for plick graph Pn(G); n ≥ 1 to have coarseness number one.