We propose a generalized Debye-Hückel (DH) theory using a recent Poisson-Fermi model that accounts for the steric, correlation, and polarization effects of ions and water treated as nonuniform spheres with interstitial voids. The generalized DH theory reduces to the classical one when these effects are not considered. The Debye length is also generalized to include the steric effect. The new theory yields an electrolyte (analytical) equation of state for calculating the activity coefficient of aqueous electrolyte solutions, which is of fundamental importance in thermodynamic modeling for a variety of chemical and biological systems. Results obtained by the analytical equation well fit experimental data for eight 1:1 and six 2:1 electrolytes with only three adjustable parameters. By contrast, the DH models extended from the classical DH theory such as the Pitzer model can have several to great many parameters due to explosive combinations of wide ranges of composition, temperature, and pressure.