We show that anisotropic negative effective dispersion relation can be achieved in pure dielectric rod-type metamaterials by turning from the symmetry of a square lattice to that of a rectangular one. Theoretical predictions and conclusions are verified by both numerical calculations and computer based simulations. The proposed anisotropic metamaterial, is used to construct a refocusing slab lens and a subdiffraction hyperlens. The all-dielectric origin makes it more straightforward to address loss and scaling, thus facilitating future applications in both the terahertz and optical range.