For the study of high-temperature superconductors and for the application of superconductivity, a superconducting high-field magnetization system with a hybrid superconducting coil was designed. This coil is composed of superconducting wires of three kinds-HTS YBCO 2G-wire, high-field and low-field NbTi wires. Three principal purposes of building this system are to inspect the characteristics of disk-shape bulk YBCO, to develop a HTS-bulk undulator, and to magnetize a portable HTS-bulk high-field magnet for application to a resonant X-ray scattering experiment. With four steps of temperature decrease, a two-stage GM-type cryocooler and liquid nitrogen provide cooling for the magnetization system. The hybrid superconducting coil, two cryogenic systems for the magnetization system and the portable HTS-bulk magnet, and the control and monitor systems that were designed are discussed.