  For a given graph $H$, the Ramsey number $r(H)$ is the minimum $N$ such that
any 2-edge-coloring of the complete graph $K_N$ yields a monochromatic copy of
$H$. Given a positive integer $n$, a \emph{fan }$F_n$ is a graph formed by $n$
triangles that share one common vertex. We show that ${9n}/{2}-5\le r(F_n)\le
{11n}/{2} + 6$ for any $n$. This improves previous best bounds $r(F_n) \le 6n$
of Lin and Li and $r(F_n) \ge 4n+2$ of Zhang, Broersma and Chen.
