Abstarct: Nowadays, electrical power system has a very important role in human life. Because of this, electrical engineering always should prepare normal operation of power system. Short circuit faults are one of the main reasons that lead to abnormal operation of system. A rapid and accurate method for fault classification is very necessary to system restoration and fault location. In addition by extending smart power grids, a fast and intelligent fault classification method is very necessary. This work presents a new and more applicable method for fault classification and faulted phase selection. In this method an innovative criteria was defined for fault classifying. This parameter is a vector that made of three phase voltage and current phasors. Using this criteria parameter, the fault classification problem lead to a vector classification problem. This new problem was solved by using Self-Organizing Map (SOM) neural networks. The proposed method was applied to a 4-bus test power system. Simulation results show that proposed method is a rapid and accurate method for fault classification. It can classify the faults in half cycle after fault starting.