A superconducting magnet with a magnetic energy of E = B 2/2μo [J/m3] has to overcome a magnetic force of P = B2/2μo [Pa] in the same expression. This means that a high-field 20 T superconducting magnet produces an electromagnetic force of 160 MPa. In order to stand such a large force, Nb3Sn superconducting wires are usually reinforced by the hard-copper housing as an external reinforcement method or the stainless steel winding as a mechanical backup of an outermost Nb3Sn coil. If we focus on a compact superconducting magnet like a cryocooled superconducting magnet, a high-strength superconducting wire with a small diameter size of 1- 2 mm is required. The High-Field Laboratory for Superconducting Materials, IMR, Tohoku University has developed Nb3Sn wires internally reinforced with CuNb or CuNbTi composite. These high-strength Nb3Sn wires were successfully employed to construct the unique compact cryocooled 28 T hybrid magnet and the cryocooled 18 T high-temperature superconducting magnet. In addition, we found that the prebending effect for high-strength Nb3Sn wires outstandingly improves the Tc, BC2 and Ic properties. As a next step, we intend to develop new Nb3Sn strand cables with the strong mechanical property of 500 MPa, applying the prebending effect for a future 22 T-φ400 mm room temperature bore superconducting magnet of a 50 T-class hybrid magnet.