The coexistence of superconductivity and topology holds the potential to realize exotic quantum states of matter. Here, we report superconductivity induced by high pressure in three thallium-based materials, covering the phase transition from a normal insulator (TlBiS 2 ) to a topological insulator (TlBiSe 2 ) through a Dirac semimetal (TlBiSeS). By increasing the pressure up to 60 GPa, we observe superconductivity phase diagrams with maximal critical temperature ( T c ) values at 6.0–8.1 K. Our density functional theory calculations reveal topological surface states in superconductivity phases for all three compounds. Our study paves the path to explore topological superconductivity and topological phase transitions. • Dome-like superconductivity phase diagrams are observed in three thallium-based materials • High pressure alters electronic state and induces phase transitions in this famous family • The theoretical calculations reveal topological surface states in superconductivity phase Pei et al. report pressure-induced superconductivity in three thallium-based materials, covering the phase transition from a normal insulator to a topological insulator through a Dirac semimetal. Revealed topological surface states in superconductivity phases for all three compounds pave the path to explore topological superconductivity and topological phase transitions.