The advanced big data analytical technologies and ever-expanding Internet-of-Things (IoT) devices and applications drive the new computing paradigm, Edge Computing. It significantly improves network performance by collecting and processing data locally or in a nearby edge data center. It also offers a far less expensive route to scalability, allowing service providers to expand their computing capability as needed. On the other hand, emerging network technologies, such as Software Defined Networking (SDN) and programmale data plane, can facilitate cost-efficient networking and direct network management. Such advancements introduce recent efforts to leverage these technologies by Edge Computing to further improve efficiency and reduce latency. However, However, albeit a lot of efforts have been spent on the edge computing challenges, little has been devoted from the SDN perspective. In particular, a generic framework that integrates programmable network control is still missing, yet imperatively needed. In this poster, we discuss the relevant challenges and propose an initial design of such a framework.