The Alpha Magnetic Spectrometer (AMS) is a particle detector designed to search for anti-matter, dark matter and the origin of cosmic rays in space. A superconducting magnet has been developed to generate 0.78 T field at the center. The magnet system consists of a pair of large "dipole" coils together with two series of six racetrack coils, arranged circumferentially in order to minimize the stray field. The coils, series connected, are wound with an aluminum-stabilized mono-strand NbTi conductor and are cooled by a superfluid helium circuit. The superconducting magnet was successfully tested up to the operating current of 410 A, however the decision was taken to equip the spectrometer with a NdFeB permanent magnet in order to maximize the experiment life. The paper describes the results of the superconducting magnet tests and in particular analyses an anomalous increasing of the coil temperature during magnet charging.