We have carried out thermally stimulated current (TSC) measurements with the current flowing along the layer on as-grown TlInS2 layered single crystals in the low temperature range 10 - 110 K with different heating rates of 0.1 - 1.5 K/s. Experimental evidence was found for the presence of two shallow electron trapping centers with activation energies of 12 and 14 meV. Their capture cross sections have been determined as 2.2 x 10(-23) and 7.1 x 10(-25) cm(2), respectively. It was concluded that retrapping in these centers is negligible, which was confirmed by the good agreement between the experimental results and the theoretical predictions of the model that assumed slow retrapping. An exponential distribution of electron traps was revealed from the analysis of the TSC data obtained at different light excitation temperatures. This experimental technique provided a value of 27 meV/decade for the trap distribution. The parameters of the monoclinic unit cell were determined by studying the X-ray powder diffraction.