A recent trend known as NFV attempts to replace dedicated hardware appliances with generic compute, storage, and network resources. NFV based on SDN can extend programmability and flexibility features of advanced network functions. Many of these network functions, however, need concrete state information to effectively process network flows. However, OpenFlow only provides a simple "match-action" paradigm and lacks the function of stateful processing in the SDN data plane, which limits its support of advanced network functions. Heavily relying on SDN controllers for all state maintenance incurs both scalability and performance issues. In this article, we propose a novel SDPA for the SDN data plane. A co-processing unit, the forwarding processor, is designed for SDN switches to manage state information through new instructions and state tables. We demonstrate the practicality and feasibility of our approach through a proof-of-concept implementation of VNFs, a stateful firewall based on SDPA. Experimental results show that VNFs which need to process state information can be supported well by the SDPA architecture, and the forwarding efficiency is improved.