  An isometry of a Finsler space is called Clifford-Wolf translation
(CW-translation) if it moves all points the same distance. A Finsler space $(M,
F)$ is called Clifford-Wolf homogeneous (CW-homogeneous) if for any $x, y\in M$
there is a CW-translation $\sigma$ such that $\sigma (x)=y$. We prove that if
$F$ is a homogeneous Finsler metric on the sphere $S^n$ such that $(S^n, F)$ is
CW-homogeneous, then $F$ must be a Randers metric. This gives a complete
classification of CW-homogeneous Finsler metrics on spheres.
