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Based on the theoretical results derived from pseudopotential method and local approximation,this paper studies the thermodynamic stability of a weakly interacting Fermi gas trapped in a harmonic potential by using analytical method of thermodynamics.The effects of the interparticle interactions as well as exteal potential on the thermodynamic stability of the system are discussed.It is shown that the system is stable as for the complete average,but as for local parts,the system is unstable anywhere.This instability shows that the stability conditions of mechanics cannot be satisfied anywhere,and the stability conditions of thermostatics cannot be satisfied somewhere.In addition,the interactions and exteal potential have direct effects on the local stability of the system.