An event-driven sensor network composed of a large number of sensor nodes has been widely studied. A sensor node sends packets to a sink when the node detects an event. For the sink to receive packets it fails to acquire, the sink needs to send re-transmission requests to the sensor node. To send the requests to the sensor node using unicast, the address of a sensor node is necessary to distinguish the sensor node from others. Since it is actually difficult to allocate the address manually to a number of nodes, a reasonable option is to use existing automatic address allocation methods. However, the methods waste the limited energy of the sensor nodes due to using a number of control messages to allocate a permanent address to every node. In this paper, we propose an energy-efficient address allocation method for the event-driven sensor network, and implement and evaluate the proposed method. The proposed method allocates a temporary address only to a sensor node which detects an event, on an on-demand basis. By performing simulation studies, we evaluated the proposed method and compared it with one of the existing methods from the perspective of the number of control messages for the address allocation. The results show that the number of control messages of the proposed method is small compared to that of the existing methods. We also evaluated the processing time overhead of the proposed method using the implemented system. Although the proposed method has little extra overhead, the results show the processing time is short enough for practical use.