A graph is outerplanar if it has a crossing-free embedding in the plane such that all vertices are on the boundary of its outer face. An outerplanar graph is maximal outerplanar if no edge can be added without losing outerplanarity. The Wiener index of a graph G is the sum of distances between all pairs of vertices of G. We show that for a maximal outerplanar graph G on n vertices, W(K₁∨P_n−1) ≤W(G)≤W( $P_n^2$), where K₁∨P_n−1 is the graph obtained from joining a vertex to each vertex of P_n−1 and $P_n^2$ is the square of P_n.