In this paper, we have proposed effective gradient refractive index structures at terahertz frequencies, which function as a planar lens, focusing reflector, and a generalized Luneburg lens (GLL). We base the structures on planar and cylindrical graphene-dielectric multilayer metamaterials. The structures are designed by tailoring the surface conductivity of the graphene layers to provide a given phase profile along with the structures. Therefore, the customizable focus area of the focusing devices, and the tunable terahertz jet effect that is produced by the GLL result. The proposed structures have potential applications in terahertz imaging, sensing, detecting, and communication areas.