A semi-active controller is designed for the nonlinear vibration suppression of a novel square-celled sandwich plate with a multi-zone magnetorheological elastomers (MRE) filler core that can spontaneously generate a magnetic field using the embedded spiral coil. First, the nonlinear dynamic model of the square-celled sandwich plate with multi-zone MRE filler core is constructed by employing the nonlinear MRE model, the equivalent theory of material mechanics, the sandwich plate theory, the virtual spring technology, the eigenvalue increment method, and the modified Fourier-Ritz method. Next, based on the Newmark-Beta approach, the displacement and acceleration responses of the dynamic system are obtained. Afterwards, the high-order differential equation of the dynamic system is derived based on the relation of input and output of the dynamic system. A reference state of the dynamic response is predefined, and then the transfer function with respect to current can be identified. Furthermore, the verifications of the proposed model and controller are conducted. With the validated model, the optimal design of the semi-active controller is provided, and the feasibility of various control strategies is also discussed in detail.