Enhancing the magnetoelectric coupling in a strain-mediated multiferroic composite structure plays a vital role in controlling magnetism by electric fields. An enhancement of magnetoelastic coupling between ferroelectric single crystal (011)-cut [Pb(Mg1/3Nb2/3)O3](1-x)-[PbTiO3]x (PMN-PT, x≈ 0.30) and ferromagnetic polycrystalline Ni thin film through an interposed benzocyclobutene polymer thin film is reported. A nearly twofold increase in sensitivity of remanent magnetization in the Ni thin film to an applied electric field is observed. This observation suggests a viable method of improving the magnetoelectric response in these composite multiferroic systems.