In this work, we addressed the application of Density Functional Theory (DFT) to determine the structural and optoelectronic properties of tetragonal TlS compound. These calculations were carried out using the Full Potential Linearized Augmented Plane Wave (FP-LAPW) approach, integrated in the Wien2k software. The optimization of the structural parameters of the TlS compound was carried out using the Generalized gradient approximation (GGA). We also determined the electronic properties using both GGA and Modified Becke-Johnson (GGA-mbj) functionals. This study revealed that TlS is a semiconductor. The energy of the indirect band gap is approximately 0.42 eV and 0.87 eV, as calculated by GGA and GGA-mbj, respectively. The value that GGA-mbj produced and the experimental value of 0.90 eV agree well. Therefore, we adopted the GGA-mbj functional in the calculation of optical properties such as complex dielectric function, optical absorption, and energy loss function. This latter study confirmed the semiconducting nature of tetragonal TlS compound and its potential use in optoelectronic devices.