In this paper, we suppose that H is a compact subgroup of locally compact topological group G and G/H is a homogeneous space which is equipped with a strongly quasi-invariant Radon measure α. Then in the group algebras L¹(G), we replace the homogeneous space G/H instead of G and consider the new Banach algebra L¹(G/H). We study this Banach algebras and it's dual. At the end, by characterization of L∞(G/H) and the left and right dual L¹(G/H)-module actions of L∞(G/H), we give a necessary and sufficient conditions for amenability and weak amenability of this Banach algebra.
