First-principles calculations predict that SrFBiS 2 has a superior birefringence of 1.28, which is larger than the giant birefringence of LaOBiS 2 [Wang H, Chin. Phys. Lett. 31 (2013)047802]. An AF layer (i.e., SrF) is shown to be important by the further investigations on AFBiS 2 (A=Mg, Ca, Ba). Here MgFBiS 2 exhibits the largest inherent birefringence (∼1.66) among single-crystal compounds. The origin of SBF is also discussed based on the electronic structure and refractive index.