The thermodynamic stability, structural and electronic properties of Te line-ordered alloys are investigated using density functional theory (DFT) methods. Thirty four possible Te line-ordered alloy configurations are found in a 5×5 supercell of a MoS2 monolayer. The calculated formation energies show that the Te line-ordered alloy configurations are thermodynamically stable at 0 K and agree very well with the random alloys. The lowest energy configurations at each concentration correspond to the configuration where the Te atom rows are far apart from each other (avoiding clustering) within the supercell. The variation of the lattice constant at different concentrations obey Vegard's law. The Te line-ordered alloys fine tune the band gap of a MoS2 monolayer although deviating from linearity behavior. Our results suggest that the Te line-ordered alloys can be an effective way to modulate the band gap of a MoS2 monolayer for nanoelectronic, optoelectronic and nanophotonic applications.