In this paper, the longitudinal dielectric function epsilon(l)(k) of primitive electrolyte solutions is discussed. Starting from a modified mean spherical approximation, an analytical dielectric function in terms of two parameters is established. These two parameters can be related to the first two decay parameters k(1,2) of the dielectric response modes of the bulk system, and can be determined using constraints of k(1,2) from statistical theories. Furthermore, a combination of this dielectric function and the molecular Debye-Huckel theory[J. Chem. Phys. 135(2011) 104104] leads to a self-consistent mean filed description of electrolyte solutions. Our theory reveals a relationship between the microscopic structure parameters of electrolyte solutions and the macroscopic thermodynamic properties, which is applied to concentrated electrolyte solutions. (C) 2015 Elsevier Ltd. All rights reserved.