We have calculated the temperature, magnetic field, and ion doping dependence of the magnetic and electric properties in Fe-doped BaTiO₃ using a microscopic model and the Green's function technique. It is shown that the ferromagnetic and multiferroic properties observed at room temperature in Fe-doped BaTiO₃ could be due to the super exchange interactions between Fe³⁺ ions in different occupational sites associated with oxygen vacancies and to the exchange coupling of Fe ions with mixed valence, Fe³⁺ and Fe⁴⁺. There is a multiferroic region which depends strongly on the Fe-doping concentration.