The electronic band structures, structural, and elastic properties of monolayer MoS2 under the biaxial strains are investigated using DFT and DFT + U methods. Significant changes in the bond distances, bond angles, electronic structures, and effective mass of electron me* (hole mh*) are observed under biaxial strain. The Bulk modulus decreases (increases) by increasing the tensile (compressive) biaxial strain. The band-gap values of unstrained 1L-MoS2 are estimated as 1.78 (1.81) eV within the GGA (GGA + U) approximations; however, direct band gap varies from 1.74 (1.76) to 1.92 (1.95) eV within a region of 0.3(0.4)% tensile to 1.13(1.11)% compressive strains. Beyond this strain region, direct nature of the band gap becomes indirect, and further increment causes semiconductor to metallic transition. Direct band-gap tuning and observed small effective mass values of electrons and holes carriers under applied strain indicate the enhanced optoelectronic properties in strained monolayer MoS2.Graphical abstract