Planar plasmonic devices are becoming attractive for myriad applications, owing to their potential compatibility with standard microelectronics technology and the capability for densely integrating a large variety of plasmonic devices on a chip. Mitigating the challenges of using plasmonics in on-chip configurations requires precise control over the properties of plasmonic modes, in particular their shape and size. Here we achieve this goal by demonstrating a planar plasmonic graded-index lens focusing surface plasmons propagating along the device. The plasmonic mode is manipulated by carving subwavelength features into a dielectric layer positioned on top of a uniform metal film, allowing the local effective index of the plasmonic mode to be controlled using a single binary lithographic step. Focusing and divergence of surface plasmons is demonstrated experimentally. The demonstrated approach can be used for manipulating the propagation of surface plasmons, e.g., for beam steering, splitting, cloaking, mode matching, and beam shaping applications.