Abstract: In this daper, the dissipative structure, synergetic and catastrophic characters of the evolution of fault system are discussed, the self-organization in fault evolution is expounded, and based on this, the significance of self-organization of fault evolution system in earthquake predi-ction is stated. The auther suggestes that the sef-organization of fault evolution system is the cardinal physical base for earthquake predi ction. Finally, basing on above-mentloned discussion, some earthquake exampl-es are given in terms of Thorns type A3 cusp catastrophe.