Recent progress in the field of topological states of matter has largely been initiated by the discovery of bismuth and antimony chalcogenide bulk topological insulators (TIs; refs ,,,), followed by closely related ternary compounds and predictions of several weak TIs (refs ,,). However, both the conceptual richness of Z2 classification of TIs as well as their structural and compositional diversity are far from being fully exploited. Here, a new Z2 topological insulator is theoretically predicted and experimentally confirmed in the β-phase of quasi-one-dimensional bismuth iodide Bi4I4. The electronic structure of β-Bi4I4, characterized by Z2 invariants (1;110), is in proximity of both the weak TI phase (0;001) and the trivial insulator phase (0;000). Our angle-resolved photoemission spectroscopy measurements performed on the (001) surface reveal a highly anisotropic band-crossing feature located at the point of the surface Brillouin zone and showing no dispersion with the photon energy, thus being fully consistent with the theoretical prediction.