Perovskite BiMnO3 with ferroelectric and ferromagnetic ordering simultaneously, as a kind of multiferroics, can be expected to have the coupling between the magnetic and dielectric properties as well as their control by the application of electric fields. This advantage can make BiMnO3 a good candidate for an artificial synapse material. Under the framework of the density functional theory, in this paper we adopt the generalized gradient approximation (GGA+U) plane wave pseudopotential method to calculate the ferroelectricity double-well potential curves and magnetic moments of Mn of tetragonal BiMnO3, with 0.18% and 4% strain exerted in its x-y plane. The results show that the magnetic moment of Mn monotonically increases from paraelectric state to ferroelectric state. It means that the ferromagnetic property of tetragonal BiMnO3 can be controlled by the intensity of polarization. The greater the stress, the greater the range of magnetic moment is. This would imply that the multiferroic artificial synapse device based on BiMnO3 can bring another degree of freedom into designing the complex cognitive systems of artificial intelligence in the future.