The nature of the spin-density wave (SDW) and its relation with superconductivity are crucial issues in the newly discovered iron-pnictide superconductors. Particularly, it is unclear whether the superconducting phase and SDW are truly exclusive from each other. We here report splittings of the band structures in Sr1-xKxFe2As2 (x=0, 0.1, 0.18), and their unusual doping dependence. Our data on single crystalline samples prove that the SDW and superconductivity could coexist in iron pnictides.