A superconducting magnet supporting and positioning system comprises a refrigerator (1), a low-temperature container (2), a cold conducting band (3), a superconducting solenoid coil (4), an upper suspension magnet (5), a side upper positioning magnet (6), a side lower positioning magnet (7), a lower suspension magnet (8) and connecting rods (9). After the superconducting solenoid coil (4) is electrified, electromagnetic repulsion is generated between the upper suspension magnet (5) and the lower suspension magnet (8) and the superconducting solenoid coil (4) to enable the superconducting solenoid coil (4) to be suspended in the air, and electromagnetic repulsion is generated between the upper side upper positioning magnet (6) and the side lower positioning magnet (7) and the superconducting solenoid coil (4) to enable the superconducting solenoid coil (4) to be positioned and free of declination. No heat contact exists between the magnets and the superconducting solenoid coil, so that transmission heat leakage of the superconducting solenoid coil can be reduced, and power of the needed refrigerator can be lowered.