There is an increasing demand for optical elements having the functionalities of hybrid devices, such as the combination of a Fresnel lens and a diffraction grating. These new devices can be used in many applications, such as in optical spectrometers, optical precision measurement systems and diffractive optical systems for enhancing the efficiency of third generation photovoltaic solar cells. There is also a growing need for developments of a cost-effective technology to fabricate compact optical devices. Therefore the motivation of our project is to find a new model of the G-Fresnel (i.e. grating and Fresnel lens) taking into account the utilization of the electromagnetic theory for the rigorous analysis of its behavior. In this paper, a novel method is proposed and employed to design a G-Fresnel device that has only one structure layer with subwavelength features, and that focuses and separates different bands of light spectra in the same focal plane. The device performance has been studied through the use of rigorous electromagnetic theory, by using the Finite Difference Time Domain (FDTD) for the study of the near field and the Angular Spectrum Method (ASM) for the study of the propagation in the far field. The optimal design of the G-Fresnel profiles depends on the profile of the Fresnel lenses that minimize the longitude chromatic aberration, and also on the diffraction grating with high first order diffraction efficiency. The verification of the G-Fresnel model that we propose shows high diffraction efficiency and a good performance in separation for a broadband light spectrum. This promising G-Fresnel model could be used to increase the efficiency of third generation photovoltaic cells.