Exploring new topological phenomena and functionalities induced by strong electron correlation has been a central issue in modern condensed-matter physics. One example is a topological insulator (TI) state and its functionality driven by the Coulomb repulsion rather than a spin-orbit coupling. Here, we report a ‘correlation-driven’ TI state realized in an organic zero-gap system α-(BETS)2I3. The surface metallic state that emerges at low temperatures exhibits characteristic transport properties of a gapless Dirac semimetal, evidencing the presence of a topological surface state in this compound. Moreover, we observe a topological phase switching between the TI state and non-equilibrium Dirac semimetal state by a dc current, which is a unique functionality of a correlation-driven TI state. Our findings demonstrate that correlation-driven TIs are promising candidates not only for practical electronic devices but also as a field for discovering new topological phenomena and phases.