The structural, electronic and optical properties of Cu₃SbS₄ with different crystalline structures have been investigated by using the PBE generalised gradient approximation and hybrid functional method (HSE06) to density functional theory at ambient and high pressure. The calculated elastic constants and phonon dispersions reveal that both the famatinite and enargite phases are mechanically and dynamically stable, except for the cubic Fm3¯m phase. The energy difference between famatinite and enargite is fairly small within the studied pressure range. Calculations on electronic band structure indicate that famatinite and enargite Cu₃SbS₄ are direct band gap materials with relatively low values of 0.39 and 0.32 eV, respectively, and the band gap increases with the increasing pressure. The optical properties calculations predict a blue-shift in the absorption edges of famatinite and enargite in response to the applied pressure.