This invention provides a new facilitated transport membrane comprising a relatively hydrophilic, very small pore, nanoporous support membrane, a hydrophilic polymer inside the very small nanopores on the skin layer surface of the support membrane, a thin, nonporous, hydrophilic polymer layer coated on the surface of the support membrane, and metal salts incorporated in the hydrophilic polymer layer coated on the surface of the support membrane and the hydrophilic polymer inside the very small nanopores, a method of making this membrane, and the use of this membrane for olefin/paraffin separations, particularly for C3=/C3 and C2=/C2 separations.