This paper deals with the exchange bias and its thermal stability in magnetic BiFeO3/Ni81Fe19 bilayer sputtered under an electromagnetic field. The results show that the BiFeO3/Ni18Fe19 bilayer presents an in-plane uniaxial magnetic anisotropy and a significant exchange bias effect, however the exchange bias field Hex in the BiFeO3/Ni18Fe19 bilayer does not show a visible training effect. The forward and recoil loop shifts towards positive fields, while holding the film in a negative saturation field. Hex decreases monotonously with the increase in the holding time (tsat), whereas Hc is almost the same. With increasing temperature Tm, Hex will not alter significantly, which means that Hex is not sensitive to the temperature, showing a good thermal stability. However, Hc may reduce rapidly with the increase in temperature. We believe that the good thermal stability may result from the coupling between ferroelectric and antiferromagnetic moments in BiFeO3.