The rapid progress of wireless communication technologies has opened a possibility to offer various types of communications to users irrespective of their locations. The all-IP based wireless networks have been proposed and the Mobile IP protocol is considered as one of prominent candidate frameworks to support a seamless mobility of users. However, to our best knowledge, there are few research efforts to design and develop a network management system targeted for Mobile IP based wireless networks. In this paper, we introduce the concept of autonomic wireless network management which utilizes SNMP agents to manage more intelligently through the self-management functionality. We present a design of autonomic wireless network management system (AWNMS) and its prototype implementation. The currently implemented system is fully compliant with Mobile IP MIB and provides management functions such as network topology auto-discovery, mobility tracking function, etc. The implemented system is validated and examined in a Wireless LAN based test-bed network.