Quek and Yap defined a relative completion A for a linear subspace A of Lp(G), 1 ≤ p < ∞ and proved that there is an isometric isomorphism, between HomL1(G), (L1(G), A) and Ã, where HomL1(G)(L1(G), A) is the space of the module homomorphisms (or multipliers) from L1(G) to A. In the present, we defined a, relative completion A for a linear subspace A of Lw p,(G), where w is a Beurling's weighted function and L wp(G) is the weighted Lp(G) space, (). Also, we proved that there is an algeabric isomorphism and homeomorphism, between HomLw1(G)(Lw1(G), A) and Ã. At the end of this work we gave some applications and examples. © TÜBİTAK.