We investigated the chemical pressure effects on structural and electronic properties of SnTe-based material using partial substitution of Sn by Ag0.5Bi0.5, which results in lattice shrinkage. For Sn1-2x(AgBi)xTe, single-phase polycrystalline samples were obtained with a wide range of x. On the basis of band calculations, we confirmed that the Sn1-2x(AgBi)xTe system is basically possessing band inversion and topologically preserved electronic states. To explore new superconducting phases related to the topological electronic states, we investigated the In-doping effects on structural and superconducting properties for x = 0.33 (AgSnBiTe3). For (AgSnBi)(1-y)/3InyTe, single-phase polycrystalline samples were obtained for y = 0–0.5 by high-pressure synthesis. Superconductivity was observed for y = 0.2–0.5. For y = 0.4, specific heat investigation confirmed the emergence of bulk superconductivity. Because the parameters obtained from specific heat analyses were comparable to In-doped SnTe, we expect that the (AgSnBi)(1-y)/3InyTe and other (Ag,In,Sn,Bi)Te phases are a candidate system for studying topological superconductivity.