Let E/F be a quadratic extension of non-archimedean local field and let G be an inner form of GL(2n, F) over F, which contains a subgroup H isomorphic to GL(n, E). In this paper we prove that (G,H) is a Gelfand pair, i.e., the H-invariant linear functional, if there exists one, on the space of an irreducible admissible representation of G is unique up to a scalar. Globally this result will play an important role in the study of H-period integrals of cusp forms on G, and its relations to the special values of automorphic L-functions.