Using the quantum statistical theory, the stability of a weakly interacting Fermi gas trapped in a strong magnetic field is investigated, the expression of stability condition is given, and the mechanisms of influences of interparticle interaction and magnetic field on the stability are analyzed. The results show that repulsive interaction will increase both the chemical potential and the space domain needed for system stability. But, the increasing of magnetic field strength will reduce the space domain needed for the system stability, and lower the stability of the particle number density distribution.