In this paper, structural, electronic, thermal, and thermoelectric properties of Al _0.25B _0.75As alloy, under pressures 0 GPa, 4 GPa and 8 GPa, have been calculated. The value of band gap at present work under 0 GPa, with GGA(PBE) exchange-correlation potential, is very close to other works with TB-mBJ method. This is a result of equal selection of muffin-tin radius spheres that are bigger than usual size for Al and B atoms. The values of band gap decrease by increasing pressure. In thermal properties, phonon contribution of heat capacity at constant volume and Debye temperature have been calculated in the range of 0K to 1000K temperatures and under 0 GPa, 4 GPa and 8 GPa pressures. Thermoelectric properties, under the same pressures and in the range of 100K to 1000K temperatures have been investigated.