The pressure induced phase transitions of OsB2 from the orthorhombic structure (Orth) to the hexagonal structure (Hex) is investigated by using ab initio plane-wave pseudopotential density functional theory, together with quasi-harmonic Debye model. We nd that the pressure-induced phase transition occurs at 2.8 GPa and 12.5 GPa by local density approximation and general gradient approximation, respectively. It is predicted that OsB2 has no phase transition temperature from the Orth structure to the Hex structure. Moreover, the dependences of the relative volume V /V0 on the pressure, thermal expansion coecient α on the pressure and temperature are also successfully obtained. The electronic properties including energy band, total and partial density of states and electron density dierence for two structures are also analyzed. The Mulliken charges and Bond populations for both Orth and Hex structures are also obtained.