As the de facto data plane technique of Software-Defined Networking (SDN), OpenFlow introduces significant programmability to enable innovative network applications. However, the simple OpenFlow data plane only maintains flow-level counters and lacks an efficient mechanism to manage network-level states, which limits its support for advanced state-aware applications. Regularly pulling whole state information from the data plane to the controller might incur untimely response to important network-level states such as CPU exhaustion, switch overload, etc and cause unnecessary traffic. To address above challenges, we introduce a novel Network-level State Management Architecture (NeSMA) to efficiently support advanced network-level state-aware applications by exploiting the opportunity of SDN central control. The data plane could be configured to check state regularly and report to the controller when triggered by state transitions. We design both sequential and parallel composition methods to deal with complex network-level states in NeSMA. To demonstrate the feasibility of our approach, we implement a software prototype of NeSMA, based on which we develop a data-center flow scheduling application. Experimental results show that NeSMA can process network-level states with low network resource consumption and high scalability without compromising packet forwarding efficiency.