Magnetoelectric (ME) sensors cannot effectively detect broadband magnetic field signals due to their narrow bandwidth, and existing readout circuits are unable to vary the bandwidth of the sensors. To expand the bandwidth, this paper introduces a negative-feedback readout circuit, fabricated by introducing a negative-feedback compensation circuit based on the direct readout circuit of the ME sensor. The negative-feedback compensation circuit contains a current amplifier, a feedback resistor, and a feedback coil. For this purpose, a Metglas/PVDF/Metglas ME sensor was prepared. Experimental measurements show that there is a six-fold difference between the maximum and minimum values of the ME voltage coefficients in the 6–39 kHz frequency band for the ME sensor without the negative-feedback compensation circuit when the sensor operates at the optimal bias magnetic field. However, the ME voltage coefficient in this band remains stable, at 900 V/T, after the charge amplification of the direct-reading circuit and the negative-feedback circuit. In addition, experimental results show that this negative-feedback readout circuit does not increase the equivalent magnetic noise of the sensor, with a noise level of 240 pT/√Hz in the frequency band lower than 25 kHz, 63 pT/√Hz around the resonance frequency of 30 kHz, and 620 pT/√Hz at 39 kHz. This paper proposes a negative-feedback readout circuit based on the direct readout circuit, which greatly increases the bandwidth of ME sensors and promotes the widespread application of ME sensors in the fields of broadband weak magnetic signal detection and DBS electrode positioning.