Magnetoelectric composites, comprising piezoelectric and magnetostrictive materials, are widely used in magnetic field sensing, energy harvesting, and transducers. This paper establishes a finite element model of a laminated magnetoelectric transducer coupled with magneto-elastic-electric fields based on the constitutive equations of the nonlinear magnetostrictive materials. Then, the resonant magnetoelectric effect under different biased magnetic fields is studied. Based on the equivalent circuit model and the two-port network theory, the magnetoelectric coefficient and the equivalent source impedance of the resonant state are solved entirely for the first time. Introducing optimized L-section matching networks between the magnetoelectric transducer and the load resistor can increase the load power and expand the operating bandwidth. The simulation results are consistent with the data from references, thus confirming the accuracy and effectiveness of the model. The simulation results demonstrate that the magnetoelectric coefficient reaches 51.79V·cm^-1·Oe^-1@51.4 kHz at a 450 Oe bias magnetic field, and reaches the ultimate output power of -3.01 dBm@50.4 kHz at a 350 Oe bias magnetic field. To ensure the load power, the power increase of 2.30 dB and the bandwidth expansion of 2.27 times are achieved by optimizing the matching network. This paper's nonlinear finite element model takes full account of the magnetoelectric effect in the acoustic resonance state and quantifies the ultimate output power. The magnetoelectric transducer model can achieve high magnetoelectric coefficient, load power, and power density in a small volume, providing a significant advantage in terms of equilibrium. The research results are of great importance in guiding the design and performance improvement of miniaturized magnetically coupled wireless power transfer systems.