The laminated bilayer magnetoelectric (ME) composites consist of magnetostrictive and piezoelectric layers are known to have giant ME coefficient due to the high coupling efficiency in bending mode. In our previous report, the bar-shaped bilayer composite has been investigated by using a magnetoelectric-coupling equivalent circuit. Here, we propose an annular bilayer ME composite, which consists of magnetostrictive and piezoelectric rings. This composite has a much lower resonance frequency of bending mode compared with its radial mode. In addition, the annular bilayer ME composite is expected to respond to vortex magnetic field as well as unidirectional magnetic field. In this paper, we investigate the annular bilayer ME composite by using impedance-matrix method and predict the ME coefficients as a function of geometric parameters of the composites.