This letter develops a self-biased magnetoelectric (ME) structure Metglas/Terfenol-D/Be-bronze/PMN-PT (MTBP) consisting of a magnetization-graded Metglas/Terfenol-D layer, a elastic Be-bronze plate, and a piezoelectric 0.67Pb(Mg1/3Nb2/3)O3-0.33PbTiO3 (PMN-PT) plate. By using the magnetization-graded Metglas/Terfenol-D layer and the elastic Be-bronze plate, multi-peak self-biased ME responses are obtained in MTBP structure. The experimental results show that the MTBP structure with two layers of Metglas foil has maximum zero-biased ME voltage coefficient (MEVC). As frequency increases from 0.5 to 90 kHz, eleven large peaks of MEVC with magnitudes of 0.75-33 V/(cm Oe) are observed at zero-biased magnetic field. The results demonstrate that the proposed multi-peak self-biased ME structure may be useful for multifunctional devices such as multi-frequency energy harvesters or low-frequency ac magnetic field sensors.