The authors propose an approach to the design of negative-refractive-index materials based on the use of dielectric rods with a gradient of the dielectric constant. A triangular-lattice photonic crystal assembled from multilayer dielectric rods with a refractive index approximating a fish-eye profile is shown to exhibit a negative refractive index in the wavelength range defined by the inequality 0.67<aλ<0.83, where a is the lattice constant of the photonic crystal. A lens consisting of a plane-parallel slab of such a photonic crystal slab is shown to be able to form an image of a point source in this wavelength range. According to the calculations, particularly high-quality images can be obtained at the wavelength λ= (32) a, where the fish-eye dielectric rods scatter the light like a medium with the refractive index equal to -0.85.