Let G be a locally compact group and H be a compact subgroup of G. We consider the homogeneous space G/H equipped with a strongly quasi-invariant Radon measure µ which arises from a rho-function. We introduce a new Beurling algebra L1 ω(G/H), where ω is a weight function on the homogeneous space G/H. Then we study the structure of this Beurling algebra. As example, we show that L1 ω(G/H) may be identified with a quotient space of L1 ω◦q(G) where q : G → G/H is the canonical quotint map. Also, we prove that L1 ω(G/H) can be considered as a Banach subalgebra of L1 ω◦q(G). Finally, by using these facts, we show that L1 ω(G/H) is a Lau algebra.
