Non-planar morphology is a common feature of devices applied in various physical fields, such as light or fluid, which pose a great challenge for surface nano-patterning to improve their performance. The present study proposes a discretely-supported nanoimprint lithography (NIL) technique to fabricate nanostructures on the extremely non-planar surface, namely high-spatial-frequency stepped surface. The designed discretely imprinting template implanted a discretely-supported intermediate buffer layer made of sparse pillars arrays. This allowed the simultaneous generation of air-cushion-like buffer and reliable support to the thin structured layer in the template. The resulting low bending stiffness and distributed concentrated load of the template jointly overcome the contact difficulty with a stepped surface, and enable the template to encase the stepped protrusion as tight as possible. Based on the proposed discretely-supported NIL, nanostructures were fabricated on the luminous interface of light emitting diodes chips that covered with micrometer step electrodes pad. About 96% of the utilized indium tin oxide transparent current spreading layer surface on top of the light emitting diode (LED) chips was coated with nanoholes array, with an increase by more than 40% in the optical output power. The excellent ability of nanopatterning a non-planar substrate could potentially lead innovate design and development of high performance device based on discretely-supported NIL.