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A self-powered current sensor consisting of the magnetostrictive/piezoelectric laminate composite and the high-permeability nanocrystalline alloys is presented. The induced vortex magnetic flux is concentrated and amplified by using an optimized-shape nanocrystalline alloy of FeCuNbSiB into the magnetoelectric laminate composite; this optimization allows improving the sensitivity significantly as well as increasing the saturation of the current sensor. The main advantages of this current sensor are its large dynamic range and ability to measure currents accurately. An analytical expression for the relationship between current and voltage is derived by using the magnetic circuit principle, which predicts the measured sensitivity well. The experimental results exhibit an approximately linear relationship between the electric current and the induced voltage. The dynamic range of this sensor is from 0.01 A to 150 A, and a small electric current step-change of 0.01 A can be clearly distinguished at the power-line frequency of 50 Hz. We demonstrate that the current sensor has a flat operational frequency in the range of 1 Hz–20 kHz relative to a conventional induction coil. The current sensor indicates great potentials for monitoring conditions of electrical facilities in practical applications due to the large dynamic range, linear sensitivity, wide bandwidth frequency response, and good time stability.