In this report, a molecular Debye-Hückel theory for ionic fluids is developed. Starting from the macroscopic Maxwell equations for bulk systems, the dispersion relation leads to a generalized Debye-Hückel theory which is related to the dressed ion theory in the static case. Due to the multi-pole structure of dielectric function of ionic fluids, the electric potential around a single ion has a multi-Yukawa form. Given the dielectric function, the multi-Yukawa potential can be determined from our molecular Debye-Hückel theory, hence, the electrostatic contributions to thermodynamic properties of ionic fluids can be obtained. Applications to binary as well as multi-component primitive models of electrolyte solutions demonstrated the accuracy of our approach. More importantly, for electrolyte solution models with soft short-ranged interactions, it is shown that the traditional perturbation theory can be extended to ionic fluids successfully just as the perturbation theory has been successfully used for short-ranged systems.