Guiding and nanofocusing of a two-dimensional (2D) optical beam in a negative-dielectric-gap waveguide is studied theoretically. An index-guiding method along the dielectric core embedded in the negative-dielectric-gap is proposed and the confinement properties of the 2D optical beam are studied by the effective-refractive-index method and FDTD simulations. We have shown that the lateral beam width of the 2D optical beam can be shrunk to zero beyond the diffraction limit. A tapered negative-dielectric-gap waveguide using adiabatic propagation achieves nano-focusing and can be applied to nano-optical couplers. This is a gateway from conventional dielectric waveguides to nano-optical integrated circuits.