The magnetoelectric (ME) composite with the flux concentration effect is designed, fabricated, and characterized for detecting weak ac magnetic-field. The high-permeability Fe73.5Cu1Nb3Si13.5B9 (FeCuNbSiB) foils act as flux concentrators and are bonded at the free ends of traditional ME laminates. With the improved ME responses in the proposed ME composite based on the flux concentration effect, the output sensitivities under zero-biased magnetic field can reach 7 V/Oe and 15.8 mV/Oe under the resonance frequency of 177.36 kHz and the off-resonance frequency of 1 kHz, respectively. The results indicate that the proposed ME composites show promising applications for high-sensitivity self-biased magnetic field sensors and ME transducers.