Titanium dioxide is one of the most popular compounds among simple oxides. Except for the fully oxidized titanate, titanium oxides have partially filled d states and their exotic properties have captured attention. Here, we report on the discovery of superconductivity in Ti4O7 and γ-Ti3O5 in a thin film form. The epitaxial Ti4O7 and γ-Ti3O5 thin films were grown using pulsed-laser deposition on (LaAlO3)0.3–(SrAl0.5Ta0.5O3)0.7 and α-Al2O3 substrates, respectively. The highest superconducting transition temperatures are 3.0 K and 7.1 K for Ti4O7 and γ-Ti3O5, respectively. The mechanism behind the superconductivity is discussed on the basis of electrical measurements and previous theoretical predictions. We conclude that the superconductivity arises from unstabilized bipolaronic insulating states with the assistance of oxygen non-stoichiometry and epitaxial stabilization.