  In this paper, we prove that for every Finsler $n$-dimensional sphere
$(S^{n},F)$ with reversibility $\lm$ and flag curvature $K$ satisfying
$\left(\frac{\lm}{1+\lm}\right)^2<K\le 1$, either there exist infinitely many
closed geodesics, or there exist at least two elliptic closed geodesics and
each linearized Poincar\'{e} map has at least one eigenvalue of the form
$e^{\sqrt{-1}\th}$ with $\th$ being an irrational multiple of $\pi$.
