Organic–inorganic hybrid lead perovskites have made rapid progress in photovoltaic fields. However, the toxicity and poor long-term stability of these materials still limit their further commercial application. Herein, we proposed a system of lead-free mixed-anion perovskites in which a chalcogen element is incorporated into the perovskite octahedrons to improve the system stability. We performed first-principles calculations of the band gaps of 192 lead-free mixed-anion perovskites belonging to the class of ABX′X″2 where A = Cs+, CH3NH3 +, and HC­(NH2)2 +; B = Ga3+, In3+, Sb3+, and Bi3+; X′ = O2–, S2–, Se2–, and Te2–, and X″ = F–, Cl–, Br–, and I–. The band gap shows a linear relationship with the average anion electronegativity. The contribution of anions to the band-edge states is related to electron affinity and structure parameters. Considering multiple factors forming perovskites, we screened out a promising candidate, CsInOBr2, with a suitable band gap (1.3 eV) for application in photovoltaics.