This paper develops a self-biased magnetoelectric (ME) heterostructure FeCuNbSiB/Ni-PZT-FeCuNbSiB/Ni (FN-P-FN) by bonding magnetization-graded FeCuNbSiB/Ni layers at the free ends of piezoelectric Pb(Zr,Ti)O3 (PZT) plate. By using the magnetization-graded magnetostrictive layer and end-bonding heterostructure, giant self-biased ME responses and obvious hysteresis are observed in FN-P-FN heterostructure. The experimental results show that the zero-biased ME voltage coefficient of FN-P-FN heterostructure reaches ∼183.2 (V/cm Oe), which is ∼2.1, ∼4.5, and ∼41.6 times higher than that of FeCuNbSiB/Ni/PZT, Ni-PZT-Ni, and FeCuNbSiB-PZT-FeCuNbSiB composites, respectively. The results indicate that the proposed three-phase end-bonding heterostructure shows promising applications for high-sensitivity self-biased magnetic field sensors and ME transducers.