In this paper, by employing first principles calculations, a two dimensional global minimum structure of Lithium Sulfide (Li2S) was predicted with a wide direct band gap and an inversed sandwich structure 1T-MoS2. The electronic properties investigations reveal that the predicted Li2S monolayer has a strain tunable direct band gap of 3.20 (4.05 eV) computed by PBE (HSE06) theory. As a wide band gap (WBG) semiconductor that is stable at high temperatures, this monolayer may have many applications in electronics and optoelectronics devices. Furthermore, the presence of a narrow phonon band gap between acoustic and optical modes suggests its application in opto-mechanical resonators.