Providing end-to-end delay guar-antees in traditional Intet is a complex task due to the distributed nature of TCP/IP protocols. Software Defined Networking (SDN) gives a new dimension to improve QoS(Quality of Service) as it can benefit from its flexibility, programmability and centralized view. In this paper, we provide delay-guar-anteed data transmission service instead ofbest efforts service for a topic-based pub-lish/subscribe system by means of exploring these specific features of SDN. We attribute this routing problem in such conditions to Delay-Constraint Lowest Cost Steiner Tree (DCLCST) problem. To solve it, we compute the shortest delay paths from source node to every subscribe node and the shortest cost paths from every subscribe node to any other node using dijkstra algorithm. Then we con-struct a delay-constraint least cost steiner tree for per-topic based on these paths as multicast tree. We also present experimental results to demonstrate the effectiveness of the algo-rithms and methods we proposed.