  In this paper, we study normal homogeneous Finsler spaces. We first define
the notion of a normal homogeneous Finsler space, using the method of isometric
submersion of Finsler metrics. Then we study the geometric properties. In
particular, we establish a technique to reduce the classification of normal
homogeneous Finsler spaces of positive flag curvature to an algebraic problem.
The main result of this paper is a classification of positively curved normal
homogeneous Finsler spaces. It turns out that a coset space $G/H$ admits a
positively curved normal homogeneous Finsler metric if and only if it admits a
positively curved normal homogeneous Riemannian metric. We will also give a
complete description of the coset spaces admitting non-Riemannian positively
curved normal homogeneous Finsler spaces.
