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One of the most important advantages of graphene is the capability of dynamically tuning its conductivity by means of chemical doping or gate voltage. Based on this property, we propose a planar gradient index graphene-based lens transforming spherical waves of the transverse-magnetic (TM) surface plasmon polariton (SPP) wave to plane waves of the TM SPP wave with specific beam deflections. Using numerical simulations, it is confirmed that a single-atomic-layered graphene can be a platform for planar gradient-index lens, which can be applied to modulate the propagation of SPP waves.