In this paper, we study the effect of uniaxial and biaxial strain on the structural and electronic properties of MoS2 monolayers by first-principle calculations based on density functional theory. Our calculations show that the bond length between Mo and S atoms dMo-S depends linearly on the strain. At the equilibrium state, MoS2 has a direct band gap of 1.72 eV opening at the K-point. However, an indirect–direct band gap transition has been found in MoS2 monolayer when the strain is introduced. MoS2 becomes a semiconductor with an indirect band gap when the uniaxial strain εx≥1% or the biaxial strain εxy≥1%. Under biaxial strain, a metal–semiconductor transition occurs at 18% of elongation. The indirect character and phase transition will largely constrain application of MoS2 monolayer to electronic and optical devices.