In this work, we study the optical properties of spherical quantum dots by using Tietz potential. In this regard, we have applied Nikiforov–Uvarov (NU) technique and numerically solved the Schrödinger equation to obtain energy levels and wave functions. Then, by using the density matrix method, we have derived expressions for the changes in linear and third-order nonlinear absorption coefficients and refractive index. According to the results obtained from this work, it is deduced that: (i) the total refractive index and the absorption coefficients increase and shift towards higher energies as $v_{0}$ increases; (ii) the total absorption coefficient and refractive index decrease and also shift towards lower energies as $r_{0}$ increases.