A network management apparatus and method are provided to easily manage devices that are dynamically added to a network and yet maintain an existing network management structure. The network management apparatus includes a device connection management unit which determines whether to extend a predetermined management information base (MIB) according to an object identifier (OID) of a device connected to a network, and a virtual MIB connection unit which creates an object ‘virtual’ in the predetermined MIB according to the determination results provided by the device connection management unit, creates a virtual object for the device under the object ‘virtual’, assigns a serial number to the virtual object for the device according to a time in which the device has been connected to the network, and redefines the OID of the device according to the serial number.