In 1974, Andrásfai, Erdős, and Sós obtained a well-know result that every $n$-vertex graph $G$ with odd girth at least $2k+1$ and minimum degree $\delta(G)>\frac{2n}{2k+1}$ is bipartite. In 2015, Messuti and Schacht proved that every $n$-vertex graph $G$ with odd girth at least $2k+1$ and $\delta(G)>\frac{3n}{4k}$ is homomorphic to $C_{2k+1}$, which genrealized the results of Häggkvist and of Häggkvist and Jin for the cases $k=2$ and $k=3$. In this paper, we extend the above results and show that every $n$-vertex graph $G$ with odd girth at least $2k+1$ and $\delta(G)>\frac{4n}{6k-1}$ is homomorphic to the Möbius ladder of size $4k$. This answers a question of Messuti and Schacht.