We consider a locally compact group G with a closed subgroup H for which G/H possesses a relatively invariant Radon measure μ. For each 1£p£+¥, we offer a construction of a left Banach L1(G)-module to the Banach space of m-measurable complex-valued functions on G/H whose pth powers are integrable. We investigate some properties of theses spaces and show that it has a left approximate identity as a left Banach L1(G)- module, where 1£p<+¥.