Optical diodes are fundamental elements for optical computing and information processing. Attempts to realize such non-reciprocal propagation of light by breaking the time-reversal symmetry include using indirect interband photonic transitions, the magneto-optical effect, optical nonlinearity or photonic crystals. Alternatively, asymmetric reciprocal transmission of light has been proposed in photonic metamaterial structures for either circularly or linearly polarized waves. Here we employ the recent concept of gradient index metamaterials to demonstrate a waveguide with asymmetric propagation of light, independent of polarization. The device blocks both transverse electric and magnetic polarized modes in one direction but transmits them in the other for a broadband spectrum. Unlike previous works using chiral properties of metamaterials, our device is based on the principle of momentum symmetry breaking at interfaces with phase discontinuities. Experiments in the microwave region verify our findings, which may pave the way to feasible passive optical diodes.