We have been developing high-strength Nb3Sn strand cables to construct a high-field superconducting outsert for a 45 T hybrid magnet with a 25 T water-cooled resistive magnet. Evidence for cold work strengthening of repeated bending treatment (prebending effect) on Nb3Sn strands internally reinforced with CuNb stabilizer, which exhibits significant enhancement of the critical current density, has been found in the superconducting magnet fabrication process using a react-and-wind method. The strand cables were designed by controlling the constituent number of CuNb/Nb3Sn strands with the prebending effect and stainless steel strands, which are expected to have a stress limit 580 MPa at 0.4% strain. In order to design a compact superconducting outsert, high-strength strand cables are adopted in a magnetic field region below 14 T to maintain relatively large engineering current densities (Je). In a higher-field region above 14 T, YBa2Cu3O7 (Y123) coated conductors are employed for an insert coil. Using combination of Y123, Nb3Sn and NbTi superconductors, a 20 T superconducting outsert with a room temperature bore of 400 mm consisting of three layers made of Y123, two layers of CuNb/Nb3Sn and two layers of NbTi was designed. The coil parameters are 440 mm inner diameter, 1080 mm outer diameter and 1138 mm coil height. A very compact 20 T superconducting outsert with a stored magnetic energy 72 MJ at an operation current 903 A can be developed for a 45 T hybrid magnet.