This paper studies Randers metrics on homogeneous Riemannian manifolds. It turns out that we can give a complete description of the invariant Randers metrics on a homogeneous Riemannian manifold as well as the geodesics, the flag curvatures. This result provides a convenient method to construct globally defined Berwald space which is neither Riemannian nor locally Minkowskian and gives another explanation of the example of Bao et al (1999 An Introduction to Riemannian-Finsler Geometry (Berlin: Springer)).