Tantalia (Ta2O5) is an interesting material which is used in several technological applications. In particular, this wide gap semiconductor is used as a new material for memristive devices, which could provide a paradigm shift on the memory devices fabrication. These new devices would be faster, denser and less power consuming than those available today. Because of this, we present a study of the optical and dielectric properties of β-Ta2O5 polymorph by means of first-principles Density Functional Theory calculations. Taking as a starting point the Nashed's model of the crystal structure of β-Ta2O5 and the generalized gradient approximation (GGA-PBEsol), we calculated the equation of state (EOS) of this polymorph. From EOS we identify the equilibrium volume and for this we calculated the frequency dependent dielectric tensor, refractive index (n = 2.63), absorption coefficient and transmittance. Also, we calculated the electronic (ε∞ = 6.98) and ionic contribution (ε0 = 43.51) to static dielectric constant and it was compared with some reported values in the literature.