The application domain of composite multiferroic materials with magnetoelectric coupling has been widening on the nano-, micro- and macro-scales. Generally, a composite multiferroic material consists of two, or more, layers of a piezoelectric material and a magnetostrictive material. In turn, the proliferation of multiferroics in more applications is accompanied by a keen focus on understanding the effect of material phases, geometry, bonding interface and arrangement of phases by performing theoretical, numerical and experimental studies to fundamentally elucidate the response. In this experimental study, a focus is given to exploit the effect of the polarization direction of the piezoelectric phase on the overall converse magnetoelectric (CME) response of a composite concentric PZT/Terfenol-D structure. Specifically, radially and axially polarized PZT rings were concentrically bonded to the outer surface of two Terfenol-D rings, respectively. It was found that the maximum, near resonance, CME coefficient of the axially-poled configuration is 443 mG V−1 when tested at 34 kHz, 80 kV m−1 electric field and 784 Oe bias magnetic field. On the other hand, the near resonance CME value for the radially-poled configuration remained nearly constant at 281.9 ± 5.3 mG V−1 between bias magnetic fields of 532 Oe and 1524 Oe at AC electric field of 80 kV m−1 with a frequency of 36 kHz. Interestingly, the CME coefficient of radially-poled composite structure exhibits a saturation behavior, while the CME coefficient for axially-poled structure is distinguished by a single peak. The difference in the response is attributed to the amount strain transduction due to the polarization direction.