In Home Area Network (HAN) of the smart grid, Power Line Communication (PLC) technology and ZigBee communication technology can be used in the communication among the Advanced Metering Infrastructure (AMI) devices. However, according to performance evaluation results of the PLC technology, we find that using the PLC technology is unsuitable for the remote meter reading service. It is worth noting that some parts of the PLC are converted to the ZigBee communication technology in Jeju, Korea. Compared with PLC, ZigBee has no restriction of the place, where the equipments can be freely set up, due to the advantage of radio communication. However, number of usable devices will impact the network performance which is depended on the address assignment. In addition, due to the restriction of transmission range among devices, it is difficult to apply the ZigBee address assignment method to the practical circumstance. In this paper, we examine the previous ZigBee address assignment schemes and the corresponding routing algorithms, and propose a novel address assignment scheme compared with the existing methods, the performance of the proposed one is improved. In particular, evaluation results show that the proposed scheme reduces the average number of hop count, the transfer time and the processing time.