Abstract. Wiener index is the sum of all distances in a graph. If there is not a directed u-v path in a digraph, we set the distance being 0. Among directed graphs, directed cycle has the largest Wiener index. We show that the second largest Wiener index is achieved by a directed n-cycle with an extra arc, so that the graph contains a 2-cycle. And among antisymmetric digraphs, the second largest Wiener index is achieved by a directed n-cycle with an extra arc, so that the graph contains a directed 3-cycle.