Video conferencing is one of the advanced technologies for users that allows online communication despite long distances. High quality communication and ongoing support for the principles of video conferencing service that can be achieved through Software-Defined Networking (SDN). SDN is a new architecture for computer networks that separates the control plane from the data plane to improve network resources and reduce operating costs. All routing decisions and control mechanisms are made by a device called a controller. Traffic engineering can be well implemented in SDN because the entire network topology is known to the controller. Considering SDN features, user requests can be dynamically routed according to current network status and Quality of Service (QoS) requirements. In general, the purpose of SDN routing algorithms is to maximize the acceptance rate of user requests by considering QoS requirements. In this literature, most routing studies to provide satisfactory video conferencing services have focused solely on bandwidth. Nevertheless, some studies have considered both delay and bandwidth constraints. In this paper, a Fuzzy Delay-Bandwidth Guaranteed Routing (FDBGR) algorithm is proposed that considers both delay and bandwidth constraints in routing. The proposed fuzzy system is based on rules that can postpone requests with high resource demands. Also, the purpose of the FDBGR is to distribute the network workload evenly for all requests, where this is done by maintaining the capacity to accept future requests. The combination of conventional routing algorithms and SDN provides remarkable improvements in mobility, scalability and the overall performance of the networks. Simulations are performed on different scenarios to evaluate the performance of the FDBGR compared to state-of-the-art methods. Besides, FDBGR has been compared with a number of most related previous works such as H-MCOP, MH-MCOP, QoMRA, QROUTE and REDO based on criteria such as number of accepted requests, average path length, energy consumption, load balancing, and average delay. The simulation results clearly prove the superiority of the proposed algorithm with an average delay of 48 ms in different topologies for video conferencing applications.