We employ the first-principles plane wave method in the frame of density functional theory (DFT) to investigate the equilibrium lattice structure, the mechanic, thermodynamic and electronic properties of CuAlSe2 compound. The lattice constants, the bulk modulus B0 and its pressure derivative B0’ are calculated. Based on the quasi-harmonic Debye model, we also obtain thermal expansion coefficient. It is noteworthy that the variation tendencies of these parameters are investigated detailed with pressure. In addition, we also calculate the elastic constants of CuAlSe2 compound. Results show that the elastic constants C11、C33、C12 and C13 increase with increasing pressure, whereas the influences of pressure on elastic constant C44 and C66 are not obvious. The calculated elastic constants satisfy the hecriterion of mechanical until the pressure grows to more than 15GPa, which suggests the structure phase transition of CuAlSe2 may be happened. We also investigate the shear sound velocity VS, longitudinal sound velocity VL, and Debye temperature ΘE from our elastic constants, as well as the thermodynamic properties from quasi-harmonic Debye model. We obtain the dependence between the heat capacity Cv and pressure, and the same as thermal expansion coefficient α. At last, the pressure dependences of band structures and density of states are also investigated, which shows that the value of TDOS decreases with the increase of the pressure.