Abstract: Based on the first principles of density functional theory(DFT), energy band structure, state density, phonon dispersion curves, Raman spectrum and infrared spectrum of CoSb₃ under different pressures are studied. In the range of 0~20 GPa, the energy band gap increases with the increase of applied pressure, while it is still an indirect band gap semiconductor. There is still no virtual frequency in the phonon dispersion curves and the stability of the structure does not change when the pressure of 0~20 GPa is applied. In the process of applying pressure, the Raman spectrum and infrared spectrum have obvious changes, and the Raman frequency has blue shift phenomenon.