Legacy networks do not open the precise information of the network domain because of scalability, management and commercial reasons, and it is very hard to compute an optimal path to the destination. According to today's ICT environment change, in order to meet the new network requirements, the concept of software-defined networking (SDN) has been developed as a technological alternative to overcome the limitations of the legacy network structure and to introduce innovative concepts. The purpose of this paper is to propose the application that calculates the optimal paths for general data transmission and real-time audio/video transmission, which consist of the major services of the National Research & Education Network (NREN) in the SDN environment. The proposed SDN routing computation (SRC) application is designed and applied in a multi-domain network for the efficient use of resources, selection of the optimal path between the multi-domains and optimal establishment of end-to-end connections.