The normal spinel cobalt oxide Co3O4 is considered as a magnetic semiconducting material comprising of cobalt ions with two oxidation states of Co2+ and Co3+. Density Functional Theory (DFT) calculation are employed to generate the structural, electronic and optical properties using Generalized Gradient Approximation (GGA) function. The Perdew-Burke-Ernzerh for solids (PBEsol) exchange-correlation functional approach successfully predict the semiconductor behaviour of Co3O4 but severely underestimates the band gap in relation to the experimental value. The GGA+U is performed in order to treat the Co-3d states and achieve the band gap of 1.26eV which agrees with the experimental results. For optical studies, here we unveil the predicted three assumed electron transition occurring in Co3O4 for O(2p)→Co2+(t2g), O(2p)→Co3+(eg) and Co3+(t2g)→Co2+(t2g).