Fabricating micro-nano structures on nonplanar substrates is technically challenging and high cost via conventional processes. In this paper, we present a new soft UV-imprint method, along with a custom designed vacuum-assisted soft UV-imprint system that allows precise control of imprint pressure, cure time and so on. The proposed method provides a highly efficient and low-cost way to fabricate high-resolution patterning micro-nano structures on nonplanar substrates. To verify the method, we fabricated a 1600 nm pitch blazed grating on a concave substrate. First, a flexible soft mold, i.e. PDMS, is copied from a commercial planar blazed grating. Second, the soft PDMS mold is imprinted to a concave substrate through our soft UV-imprint system and the blazed grating profile is transferred to the concave substrate. Finally, the surface profile of the concave grating is tested, demonstrating that the capacity of our system to fabricate microstructures on nonplanar substrates.