When faults occur in transmission lines, the classification of faults is very important. If the fault is HIF(High Impedance Fault), it cannot be detected or removed by conventional overcurrent relays (OCRs), and results in fire hazards and causes damages in electrical equipment or personal threat. The fast discrimination of fault needs to effective protection and treatment and is important problem for power system protection. This paper propolsed the fault detection and discrimination algorithm for LIFs(Low Impedance Faults) and HIFs(High Impedance Faults). This algorithm uses artificial neural networks and variation of 3-phase maximum currents per period while faults. A double lines-to-ground and line-to-line faults can be detected using Neural Network. Also, the other faults can be detected using the value of variation of maximum current. Test results show that the proposed algorithms discriminate LIFs and HIFs accurately within a half cycle.