In this study, we investigate for the first time the electronic states and optical characteristics of GaAs quantum dot with an on-center hydrogenic impurity using a Konwent-like spherical potential well. We numerically solve the radial component of Schrodinger equation in the framework of the effective-mass approximation (EMA) to determine the energy level structure and wavefunctions of the system. We then calculate the optical absorption coefficient (OAC) of the system using Fermi's golden rule and discuss the influence of the energy separation (E1p-E1 s), the dipole matrix element and the parameters of the potential on the OAC. We calculate and compare radial distributions for the lowest four electronic states (i.e., 1 s, 1p, 2 s, and 2p) of the system with and without the on-center impurity for different values of the parameters of the Konwent-like potential. Our results show how vary the parameters of the potential to tune the OAC towards red or blue shift and also to control its amplitude.