A broadband current-sensing device with frequency-conversion mechanism consisting of Terfenol-D/Pb(Zr.Ti)O3 (PZT)/Terfenol-D magnetoelectric laminate and Fe73.5Cu1Nb3Si13.5B9 nanocrystalline flux concentrator is fabricated and characterized. For the purpose of acquiring resonance-enhanced sensitivity within broad bandwidth, a frequency-modulation mechanism is introduced into the presented device through the nonlinearity of field-dependence giant magnetostrictive materials. The presented configuration provides a solution to monitor the weak currents and achieves resonance-enhanced sensitivity of 178.4 mV/A at power-line frequency, which exhibits ∼3.86 times higher than that of direct output at power-line frequency of 50 Hz. Experimental results demonstrate that a weak step-change input current of 1 mA can be clearly distinguished by the output amplitude or phase. This miniature current-sensing device provides a promising application in power-line weak current measurement.