A novel nonlinear theoretical model is established for magnetoelectric (ME) effect in trilayer of magnetostrictive and piezoelectric phases, in which the nonlinear magnetic-mechanical coupling behavior for the magnetostrictive phase is firstly taken into account. In this theoretical model, the interface coupling parameter k is used for characterizing actual bonding conditions at the interface. The coupled magneticmechanical-electric effect involving linear and nonlinear coupling interactions in the ME laminated composites is numerically simulated using this nonlinear model. The numerical results predict giant ME effect for Terfenol-D based ME laminated composites. The quantitative dependences of the giant ME effect on the applied magnetic field, the piezoelectric property of piezoelectric phase, the volume fraction of magnetostrictive phase and the interface coupling parameter k are discussed in details. All of these dependences indicate that the nonlinear theoretical model established in this article can accurately capture nonlinear magnetic-mechanical-electric coupling behavior for Terfenol-D based ME laminated composites. The giant ME effect predicted for the Terfenol-D/PMN-PT/Terfenol-D composites is in excellent agreement with recent experimental data available. It confirms the validity and reliability of the obtained nonlinear theoretical model, and demonstrates the significance and necessity of considering the nonlinear magnetic-mechanical coupling behavior of Terfenol-D.