  In this paper, we use the flag curvature formula for homogeneous Finsler
spaces in our previous work to classify odd dimensional smooth coset spaces
admitting positively curved reversible homogeneous Finsler metrics. We will
show that the most features of L. B\'{e}rard-Bergery's classification results
for odd dimensional positively curved Riemannian homogeneous spaces can be
generalized to reversible Finsler spaces.
