We experimentally demonstrate terahertz (THz) transmission properties of the two GdBa2Cu3O7-x (GdBCO) films with the thicknesses of 105 and 58 nm grown on a LaAlO3 (LAO) single crystal substrate using a conventional pulsed laser deposition (PLD) technique. Ar-ion milling works well in thinning down to obtain 50 nm-thick films, still maintaining their superconducting property at below its critical temperature. Those thinner superconducting films are suitable to develop various optical applications combined with plasmonic nanostructures to enhance light-matter interactions in the THz and mid-infrared regions. Furthermore, this combined system would create opportunities in studying electrodynamics of Cooper pairs inside the limited volume underneath the plasmonic structures.