We present a new design of a plasmonic Luneburg lens made from a gradient-index metasurface that was constructed with an array of nanometer-sized holes in a dielectric thin film. The fabricated structure consists of a planar lens with a diameter of 8.7 μm composed of a rectangular array of holes with a periodicity of 300 nm. The experimental characterization includes leakage-radiation microscopy imaging in the direction and frequency space. The former allows for characterization of the point spread function and phase distribution, whereas the latter grants access to qualitative measurements of the effective mode indices inside the plasmonic lens. The experimental results presented here are in good agreement with the expected average performance predicted by the numerical calculations. Nevertheless, the robustness of the characterization techniques presented here is also exploited to determine deviations from the design parameters.