A challenge in the fabrication of nanostructures into non-planar substrates is to form a thin, uniform resist film on non-planar surfaces. This is critical to the fabrication of nanostructures via a lithographic technique due to the subsequent pattern transfer process. Here we report a new double transfer UV-curing nanoimprint technique that can create a nanopatterned thin film with a uniform residual layer not only on flat substrates but also on highly curved surfaces. Surface relief gratings with pitches down to 200 nm are successfully imprinted on the cylindrical surface of optical fibers, and further transferred into a SiO2 matrix using reactive ion etching (RIE), demonstrating that our technique is applicable for fabricating high-resolution nanostructures on non-planar substrates.