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Power system fault detection has been an import area of study for power distribution networks. The power transmission systems often operate in the kV range with significant current flowing through the lines. A single fault, even lasting for a fraction of a second, can cause huge losses and manufacturing downtime for industrial applications. In this research, we develop an approach to detect, classify, and localize different types of phase-to-ground and phase-to-phase faults in three-phase power transmission systems based on discrete wavelet transform (DWT) and artificial neural networks (ANN). The multi-resolution property of wavelet transform provides a suitable tool to analyze the irregular transient changes in voltage or current signals in the network when fault occurs. An artificial neural network is employed to discriminate the types of fault based on features extracted by DWT. Computer simulation results show that this method can effectively identify various faults in a typical three-phase transmission line in power grid.