In the structure of bulk acoustic wave (BAW) magnetoelectric antenna, the induced current generated by the magnetic film in the magnetostrictive layer in the high frequency magnetic field will cause eddy current loss, which in turn affects the radiation performance of the antenna. To analyze and suppress the eddy current loss of magnetic thin films, the eddy current loss model of FeGaB magnetic thin film is established by using the finite element simulation method. According to the skin effect of eddy current, the surface eddy current and internal eddy current are discussed. And eddy current suppression is carried out by inserting Al2O3 thin film to isolate the current. Through the comparative analysis of three kinds of Al2O3 film separation methods, the optimal separation methods for the surface eddy current suppression and the internal eddy current suppression are obtained. Considering the influence of the total eddy current, a cross separation method is proposed as the optimal separation method to suppress the eddy current loss. The simulation results show that the total eddy current loss can be suppressed more than 65% by using the proposed method to insert 10 nm Al2O3 thin film into the FeGaB magnetic thin film.