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A subwavelength-modulated dielectric nonlinear Lüneburg lens is proposed and numerically verified. In the linear limit, the structure focuses a plane wave to an ideal geometrical point image. In the presence of Kerr nonlinearity, focal shift to a Gaussian beam input is compensated at a tunable intensity value. Nonlinear Lüneburg lens is also capable of finite conjugate imaging. A modified aperiodic Lüneburg is also proposed to greatly reduce the aberration caused by the Kerr effect.