The present invention provides a novel lithium titanium sulfide, lithium niobium sulfide, or lithium titanium niobium sulfide that contains a sulfide containing lithium, titanium and/or niobium, and sulfur as constituent elements, and that has excellent charge-discharge performance (especially excellent charge-discharge capacity and charge-discharge potential) useful as a cathode active material or the like for lithium batteries, such as metal lithium secondary batteries or lithium-ion secondary batteries. Particularly preferred are, for example, (1) lithium titanium sulfide containing lithium, titanium, and sulfur as constituent elements and having a cubic rock salt crystal structure, (2) lithium niobium sulfide containing lithium, niobium, and sulfur as constituent elements and having a diffraction peak at a specific position in an X-ray diffractogram, and (3) lithium titanium niobium sulfide containing lithium, titanium, niobium, and sulfur as constituent elements and having a diffraction peak at a specific position in an X-ray diffractogram.