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The minimum distance of a vertex v to an set of vertices of a graph G is defined as :<br />       .<br /> The n-Wiener polynomial for this distance of a graph G is defined as<br />       ,<br /> where  is the number of order pairs (v,S), , such that<br />       ,<br /> and  is the diameter for this minimum n-distance.<br /> In this paper, the n-Wiener polynomials for some types of graphs such as complete graphs, bipartite graphs, star graphs, wheel graphs, path and cycle graphs are obtained .The n-Wiener index for each of these special graphs is given. Moreover, some properties of the coefficients of   are established.<br />