With the increase of network complexity, the flexibility of network control and management becomes a nontrivial problem. Both Software Defined Network (SDN) and Autonomic Network technologies are sophisticated technologies for the network control and management. These two technologies could be combined together to construct a software defined self-managing solution for the future network. An autonomic QoS management mechanism in Software Defined Network (AQSDN) is proposed in this paper. In AQSDN, the various QoS features can be configured autonomically in an OpenFlow switch through extending the OpenFlow and OF-Config protocols. Based on AQSDN, a novel packet context-aware QoS model (PCaQoS) is also introduced for improving the network QoS. PCaQoS takes packet context into account when packet is marked and managed into forwarding queues. The implementation of a video application's prototype which evaluates the self-configuration feature of the AQSDN and the enhancement ability of the PCaQoS is presented in order to validate this design.