We demonstrate a time-efficient and low-cost approach to fabricate Si3N4 coated nanodome structures in fluorescent SiC. Nanosphere lithography is used as the nanopatterning method and SiC nanodome structures with Si3N4 coating are formed via dry etching and thin film deposition process. By using this method, a significant broadband surface antireflection and a considerable omnidirectional luminescence enhancement are obtained. The experimental observations are then supported by numerical simulations. It is believed that our fabrication method will be well suitable for large-scale production in the future.