We propose a novel graphene-dielectric-based meta-surface for manipulating the polarization of the incident light in the terahertz regime. The proposed structure comprised two orthogonally oriented periodic array of graphene ribbons (PAGRs) which are separated by a dielectric spacer and deposited on an Au-backed dielectric substrate. Based on the transmission line theory, an equivalent model with excellent accuracy is suggested for the proposed structure. By leveraging the simplicity of the model, we design a three-state quarter wave plate that is able to dynamically switch the polarization of the reflected wave to linear, right-, and left-hand polarizations while keeping the reflected amplitude remarkably high. Thanks to the simplicity of the model, the proposed structure can be easily used for designing other metasurfaces for light propagation control applications in imaging, sensing, and telecommunication.