A theory for the frequency dependence of ionic conductivity of an electrolyte solution is presented. In this theory contributions to the conductivity from both the ion atmosphere relaxation and the electrophoretic effects are included in a self-consistent fashion. Mode coupling theory, combined with time-dependent density functional theory of ion atmosphere fluctuations, leads to expressions for these two contributions at finite frequencies. These expressions need to be solved self-consistently for the frequency dependence of the electrolyte friction and the ion conductivity at varying ion concentrations. In the limit of low concentration, the present theory reduces exactly to the well-known Debye-Falkenhagen (DF) expression of the frequency-dependent electrolyte friction when the non-Markovian effects in the ion atmosphere relaxation are ignored and in addition the ions are considered to be pointlike. The present theory also reproduces the expressions of the frequency-dependent conductivity derived by Chandra, Wei, and Patey when appropriate limiting situations are considered. We have carried out detailed numerical solutions of the self-consistent equations for concentrated solutions of a 1:1 electrolyte by using the expressions of pair correlation functions given by Attard. Numerical results reveal that the frequency dependence of the electrolyte friction at finite concentration can be quite different from that given by the DF expression. With the increase of ion concentration, the dispersion of the friction is found to occur at a higher frequency because of faster relaxation of the ion atmosphere. At low frequency, the real part of the conductivity shows a small increase with frequency which can be attributed to the well-known Debye-Falkenhagen effect. At high frequency, the conductivity decreases as expected. The extensions of the present theory to treat frequency-dependent diffusivities of charged colloid suspensions and conductivity of a dilute polyelectrolyte solution are discussed.