  In this paper, we prove that on every Finsler manifold $(M,\,F)$ with
reversibility $\lambda$ and flag curvature $K$ satisfying
$\left(\frac{\lambda}{\lambda+1}\right)^2<K\le 1$, there exist $[\frac{\dim
M+1}{2}]$ closed geodesics. If the number of closed geodesics is finite, then
there exist $[\frac{\dim M}{2}]$ non-hyperbolic closed geodesics. Moreover,
there are 3 closed geodesics on $(M,\,F)$ satisfying the above pinching
condition when $\dim M=3$.
