The superconducting solenoid with constant large current is exposed to an alternating magnetic field during the acceleration of the superconducting maglev train, which will cause flux jump of the superconducting solenoid. It can reduce the current-carrying capacity of the solenoid, and generate a lot of heat and make the temperature of the superconducting solenoid rise sharply, which will make the whole superconducting coils quenched. Thus the research of flux jump has very important scientific significance. Nb ₃Sn superconducting wire is a composite structure composed of multiple superconducting filaments、copper and epoxy resin. In this paper, the magneto-thermal instability behavior of a three-dimensional superconducting wires under alternating magnetic fields and constant current is studied by using a two-dimensional model in which the net current of each filament is constrained to zero. By analyzing the effect of amplitude and frequency of alternating magnetic field on flux jump of a Nb ₃Sn superconducting wire, we find that when the magnetic field amplitude keeps unchanged, the magnetic field threshold of the initial flux jump changes non-monotonically with the frequency. While the frequency keeps unchanged, the threshold of the initial flux jump changes monotonously with the amplitude of the alternating magnetic field. In addition, with the decreasing applied field, the frequency range for flux jump first increases then decreases to certain critical frequency when the superconducting wire does not have flux jumps. The results of this paper can provide a theoretical basis for regulating the magneto-thermal instability of superconducting wires.