Assume G is a non-abelian group which consists a set of vertices, V = {v1, v2, ..., vn} and a set of edges, E = {e1, e2, ..., em} where n and m are the positive integers. The non-commuting graph of G, denoted by ????G, is the graph of vertex set G−Z(G), whose vertices are non-central elements, in which Z(G) is the center of G and two distinct vertices are adjacent if and only if they do not commute. In addition, the Harary index of a graph ????G is the half-sum of the elements in the reciprocal distance of Dij where Dij the distance between vertex i and vertex j. In this paper, the Harary index of the non-commuting graph for dihedral groups is determined and its general formula is developed.

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