  Let $(M,F)$ be a compact connected homogeneous non-Riemannian Finsler
manifold with $\dim M>1$. We prove that any conformal vector field on $(M,F)$
is a Killing vector field. Further more, we prove that $\rho F$ is a
homogeneous Finsler metric on $M$ if and only if $\rho$ is a positive constant
function.
