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A 20 T superconducting magnet was designed and developed for studying physical properties. The cryostat is an open neck Dewar vessel with a liquid nitrogen reservoir and radiation shield. A lambda plate is built into the magnet support assembly. The operating temperature can be reduced from 4.2 K to 2.2 K by pumping liquid helium through a throttle valve under the lambda plate.The central magnetic field is 20 T at 2.5 K (18 T at 4.2 K). The field homogeneity is less than + 0.1% in a 10 mm diameter sphere volume. The inner diameter of the cold clear bore is 52 mm. The outer diameter of the coil is 349 mm. The height of the coil, excluding the magnet protection circuit, is 560.5 mm. The coil is wound with the specially developed wires for use in high magnetic fields. In the case of Nb 3 Sn wires, a marked increase of the critical current density is achieved with higher tin content in the bronze matrix. The wires are more resistant to external stress with a rectangular cross section. We hung the magnet into the Dewar vessel and energized it. At first the magnet was operated at liquid helium temperature 4.2 K. As a result, the magnetic field rose to over 18 T with no training quench. The maximum magnetic field was 18.5 T. Then we energized the magnet after reducing the operating temperature to 2.2 K. Finally, the magnetic field rose to over 20 T with no quench.The result of this study shows that this magnet delivers a high magnetic field stably and easily.Index Terms-High magnetic field, Nb 3 Sn, superconducting magnet, 20 T.