Magnetoelectric (ME) antenna operates at the acoustic wave resonance rather than EM wave resonance, thus it shows significant superiority for developing compact antennas and antenna arrays. The simulation of ME antenna involves the nonlinear coupling of Electrostatics, Solid Mechanics, and Magnetic physics, making it difficult to model such devices. This paper proposes a fully multi-field coupled model for the ME antenna, in which the nonlinear magnetostrictive model is taken into account. The nonlinear magnetization is solved and then AC and DC simulations are performed by coupling different physics. The effects of magnetic bias and pre-stress on the converse magnetoelectric (CME) coupling and near-field radiation are discussed for the first time, to regulate the performance of the ME antenna with fixed dimensions. The results indicate that the magnetic bias and pre-stress can change the resonance frequency, CME coefficient, and near-field radiation of ME antenna. Particularly, it should be noted that pre-stress has the opposite effect in the low and high regions of the bias field. The near-field radiation is significantly enhanced by applying a proper magnetic bias or pre-stress. This simulation may facilitate the understanding of nonlinear CME behavior and provide a basis for designing nonlinear active and tunable ME antenna.