Using the equation of free energy for a weakly interacting Fermi gas, the stability of a weakly interacting Fermi gas in the absence of external potential is studied by means of thermodynamics. The instability arising from the weakly attractive interacting of a Fermi gas is pointed out. The particle density criterion and the temperature criterion of instability for the imperfect Fermi gas with weakly attractive interaction are given, and the dependance of the critical density of particles on the temperature and the mass of particle and the attractive interaction is discussed.