There are provided an apparatus for fixing a plastic sheet which fixes a plastic sheet to fabricate a nano pattern and a method of fabricating a nano pattern on a plastic sheet using the same. The apparatus for fixing a plastic sheet includes: a pair of planar metal guide rings interposingly fixing a plastic sheet from above and below, respectively; and a sheet fixing chuck including: a ring fixer sucking the pair of planar metal guide rings through a vacuum groove to be fixed thereto; and a sheet fixer having a plurality of vacuum pin holes formed therein, the vacuum pin holes sucking a bottom of the plastic sheet fixed by the planar metal guide rings. The apparatus allows fabrication of the nano pattern on the plastic sheet having less roughness than that of a semiconductor substrate or a glass substrate.