Photoluminescence (PL) spectra of TlInS2 layered single crystals were investigated in the 500-860 nm wavelength region and in the 11.5-100 K temperature range. We observed two PL bands centred at 515 nm (2.41 eV, A band) and 816 nm (1.52 eV, B band) at T = 11.5 K and an excitation intensity of 7.24 W cm-2. A detailed study of the A band was carried out as a function of temperature and excitation laser intensity. A red shift of the A band position was observed for both increasing temperature and decreasing excitation laser intensity in the range from 0.12 to 7.24 W cm-2. Analysis of the data indicates that the A band is due to radiative transitions from the moderately deep donor level located at 0.25 eV below the bottom of the conduction band to the shallow acceptor level located at 0.02 eV above the top of the valence band. An energy-level diagram for radiative donor-acceptor pair transitions in TlInS2 layered single crystals is proposed.