Delafossite CuAlO2 is a p-type transparent semiconductor oxide with space group R-3m (N°166) is a material with extended applications in different fields. Structural parameters, band structure, and density of CuAlO2 have been investigated in the light of the Density Functional Theory (DFT) using PBE pseudopotentials (norm-conserving pseudopotentials). Our calculations are performed with the ABINIT package using cut-off energy of 100 Hartree, showing convergence to cut-off energy up to 30 Hartree. The lattice parameters of CuAlO2 obtained after the relaxation process are a = b = 2.904 Å and c = 17.202 Å; and consequently, volume of V=174.014 Å3 , also the derivate of the bulk modules Bo´=4.1, and bulk modulus Bo=174 Gpa were found. We find that discrepancies between our calculated lattice parameters a, c, and c/a are overestimated about 0.798%, 0.591%, and 0.219% compared to the reference’s theoretical calculations of Qi-Jun Liu et,al respectively. The calculated energy band structure of CuAlO2 and the high-symmetry points of Brillouin Zone show that the delafossite structure has an indirect band gag (~ 1.21 eV) because the top valence and the bottom conduction are found at F point and Г point, respectively. This work aims to study structural parameters, band structure, and density of states of delafossite CuAlO2 and give one application as solar cell.