To discover routes, the nodes in the ZigBee-based sensor network use a simplified AODV (Ad-hoc On-demand Distance Vector). The AODV floods RREQ (Route Request) messages to find a route to a destination. However, the flooding of RREQ causes heavy loads in the network and it leads to significant delay in packet delivery. Especially, since a large portion of traffic is transmitted from sensor nodes to a sink node, a number of redundant RREQ messages to the same sink node are generated. We propose a new route discovery algorithm to reduce the routing overhead and the delay in the event reporting. We devise an H-node, which maintains a fresh route from itself to a sink node and replies to the RREQ messages for the sink node. In addition, we modify the RREQ to include an event information of sensor nodes for rapid reporting. Our simulation results show the improvement of the proposed scheme with respect to routing overhead, latency, and energy consumption.