Abstarct: In this thesis, we study invariant finsler metrics on homogeneous manifolds. We first express preparations about homogeneous and symmetric Riemannian and Finsler structure and then give a descxription of invariant finsler metrics on homogeneous manifold and abtain a necessary and sufficient condition for a homogeneous manifold to have these metrics. as a special case, we study a necessary and sufficient condition for a lie group to have bi-invariant finsler metrics. Finally, we provide some condition for a homogeneous manifold to admit a invariant non-Riemannian Finsler metrics and present some interesting examples.