Recent progress in the field of topological states of matter(1,2) has largely been initiated by the discovery of bismuth and antimony chalcogenide bulk topological insulators (TIs; refs 3-6), followed by closely related ternary compounds(7-16) and predictions of several weak TIs (refs 17-19). However, both the conceptual richness of Z(2) classification of TIs as well as their structural and compositional diversity are far from being fully exploited. Here, a new Z(2) topological insulator is theoretically predicted and experimentally confirmed in the beta-phase of quasi-one-dimensional bismuth iodide Bi4I4. The electronic structure of beta-Bi4I4, characterized by Z(2) 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 (M) over bar point of the surface Brillouin zone and showing no dispersion with the photon energy, thus being fully consistent with the theoretical prediction.