A record-high, near-theoretical intrinsic magnetoelectric (ME) coupling of 7 V cm(-1) Oe(-1) is achieved in a heterostructure of piezoelectric Pb(Zr,Ti)O-3 (PZT) film deposited on magnetostrictive Metglas (FeBSi). The anchor-like, nanostructured interface between PZT and Metglas, improved crystallinity of PZT by laser annealing, and optimum volume of crystalline PZT are found to be the key factors in realizing such a giant strain-mediated ME coupling. [GRAPHICS] .