Flat lenses when compared to curved surface lenses have the advantages of being aberration free and they offer a compact design necessary for a myriad of electro-optical applications. In this paper we present flat and ultra-thin lenses based on graphene, the world’s thinnest known material. Monolayers and low number multilayers of graphene were fabricated into Fresnel zones to produce Fresnel zone plates which utilize the reflection and transmission properties of graphene for their operation. The working of the lens and their performance in the visible and terahertz regimes was analyzed computationally. Experimental measurements were also performed to characterize the lens in the visible regime and a good agreement was obtained with the simulations. The work demonstrates the principle of atom thick graphene-based lenses, with perspectives for ultra-compact integration.