In a typical zone-picking warehouse, the picking area is divided into many small zones. This environment has one important restriction, i.e. no more than one picker can be in the same zone at the same time. In other words, a picker cannot enter a zone that has already been occupied by another picker to perform the picking operations. In this study, we assume the zone-picking warehouse has an RFID (Radio Frequency Identification) system that allows us to have the real-time information of every picking cart's location and its order status. With this real-time information, we develop a real-time routing strategy for this zone-picking warehouse with an RFID system. The results show the proposed real-time routing strategy in a warehouse with an RFID system outperforms the dynamic routing strategy proposed by other researchers for a warehouse without an RFID system in all performance measures used by us.