A low frequency magnetoelectric (ME) response model of magnetostrictive/piezoelectric laminate composite is presented based on energy conversion principle, and ME response characteristics of different laminate structures are compared in this paper. In this model it is assumed that the energy transfer between the layers of the composite laminates is achieved by the interlayer shear force. The stresses and strains of the magnetostrictive and piezoelectric layers are analyzed by the stress function method. While the strain and stored magnetic energy of magnetostrictive layers and the strain and electric field energy of piezoelectric layers are solved. Under open-circuit conditions, the interlayer shear force and the low frequency ME response model of laminate composites are obtained by using Hamilton principle of minimum energy. The theoretical results show that the ME voltage coefficient is related to the Poisson ratio, magnetic permeability, magnetomechanical coupling coefficient of magnetostrictive material, Poisson ratio, and electromechanical coupling coefficient of piezoelectric material. The influences of these parameters are analyzed. The magnetoelectric characteristics of two- and three-tier laminated structures are compared in this paper, showing that different laminated structures have different formulas for ME coefficient and calculation errors will be smaller when the corresponding ME coefficient formula is used. The experimental results show that the analytical error is smaller than 6% and the model can better describe the low frequency ME response characteristics of laminated magnetoelectric materials.