Surface topography and refractive index profile dictate the deterministic functionality of a lens. The polarity of most lenses reported so far, that is, either positive (convex) or negative (concave), depends on the curvatures of the interfaces. Here we experimentally demonstrate a counter-intuitive dual-polarity flat lens based on helicity-dependent phase discontinuities for circularly polarized light. Specifically, by controlling the helicity of the input light, the positive and negative polarity are interchangeable in one identical flat lens. Helicity-controllable real and virtual focal planes, as well as magnified and demagnified imaging, are observed on the same plasmonic lens at visible and near-infrared wavelengths. The plasmonic metalens with dual polarity may empower advanced research and applications in helicity-dependent focusing and imaging devices, angular-momentum-based quantum information processing and integrated nano-optoelectronics.