To address the issue that existing traveling wave (TW) positioning devices in distribution networks struggle to accurately detect fault transient TWs, resulting in significant positioning errors. This paper proposes a TW fault locating method based on tunneling magnetoresistance (TMR) current sensors and develops a prototype. First, a TMR-based current measurement method is proposed. Comparative experiments on wide-band transient signal current measurements are conducted, and a compact intelligent TMR sensor with edge computing capabilities is developed to precisely capture fault transient signals. On this basis, distributed sensors are installed to measure the transient current signals in the distribution network. An improved empirical mode decomposition method is employed to reduce noise interference. Subsequently, the energy values of the decomposed signals are calculated, and the arrival time of the traveling wavefront is accurately calibrated to achieve precise fault localization. Simulation and 10kV distribution network test results demonstrate that the proposed method is an effective means of accurate positioning, the sensor devices are easy to install and exhibit significant engineering value.