Let $G=(V,E)$ be a simple connected graph with vertex set $V$ and edge set $E$. Wiener index $W(G)$ of a graph $G$ is the sum of distances between all pairs of vertices in $G$, i.e., $W(G) = \sum_{\{u,v\}\subseteq G}d_G(u,v)$, where $d_G(u,v)$ is the distance between vertices $u$ and $v$. In this note we give more precisely the unicyclic graphs with the first tree largest Wiener indices, that is, we found another class of graphs with the second largest Wiener index.