  The Tur\'an number $ex(n,H)$ is the maximum number of edges in an $H$-free
graph on $n$ vertices. Let $T$ be any tree. The odd-ballooning of $T$, denoted
by $T_o$, is a graph obtained by replacing each edge of $T$ with an odd cycle
containing the edge, and all new vertices of the odd cycles are distinct. In
this paper, we determine the exact value of $ex(n,T_o)$ for sufficiently large
$n$ and $T_o$ being good, which generalizes all the known results on
$ex(n,T_o)$ for $T$ being a star, due to Erd\H{o}s et al. (1995), Hou et al.
(2018) and Yuan (2018), and provides some counterexamples with chromatic number
3 to a conjecture of Keevash and Sudakov (2004), on the maximum number of edges
not in any monochromatic copy of $H$ in a $2$-edge-coloring of a complete graph
of order $n$.
