  An extremal graph for a graph $H$ on $n$ vertices is a graph on $n$ vertices
with maximum number of edges that does not contain $H$ as a subgraph. Let
$T_{n,r}$ be the Tur\'{a}n graph, which is the complete $r$-partite graph on
$n$ vertices with part sizes that differ by at most one. The well-known
Tur\'{a}n Theorem states that $T_{n,r}$ is the only extremal graph for complete
graph $K_{r+1}$. Erd\"{o}s et al. (1995) determined the extremal graphs for
intersecting triangles and Chen et al. (2003) determined the maximum number of
edges of the extremal graphs for intersecting cliques. In this paper, we
determine the extremal graphs for intersecting odd cycles.
