Magnetoelectric composite structures of CFO (CoFe2O4)-disk/PZT (Pb(Zr052Ti0.48)O-3)-ring and PZT-disk/CFO-ring were prepared and evaluated, where the magnetostrictive and piezoelectric phases were coupled through normal stresses. Under bias magnetic fields around 3400 Oe, the peak magnetoelectric coefficients reached 18.1 and 102.6 mV cm(-1) Oe(-1) at 1 kHz for CFO-disk/PZT-ring and PZT-disk/CFO-ring structures, respectively, which were much higher than that of the corresponding layered composite. Prediction for magnetoelectric coefficients at low frequency was conducted, and the improved interfacial mechanical coupling through normal stresses was responsible for the enhanced magnetoelectric properties of the present composite structures. Moreover, the frequency dependence of the magnetoelectric coefficient was investigated, and the resonant magnetoelectric coefficients were up to 4120 and 6430 mV cm(-1) Oe(-1) for CFO-disk/PZT-ring and PZT-disk/CFO-ring composite structures, respectively.