Abstract In recent years, multiferroics have drawn much scientific attention in the field of spintronics due to the possibility of ‘zero-current’ manipulation of magnetization. In the present study, a three- dimensional phase field model was developed to investigate strain-mediated magnetoelectric coupling in FeGa/BaTiO3 epitaxial bilayer systems. Due to strong elastic interaction, the spontaneous strain in a BaTiO3 substrate can be efficiently transferred to the FeGa ferromagnetic thin film mounted on it, which resulted in printing of the domain patterns from the former to the latter. The transferred domain structures demonstrated high stability in response to the external magnetic field. Our simulation results showed that the magnetic domain wall motion can be manipulated using ultralow voltage of less than 0.08V. Moreover, our investigation of the lateral size effects of the ferromagnetic layer demonstrated that the magnetic domain wall would not extinct even if the lateral size was reduced to tens of nanometer.