Zigbee (IEEE 802.15.4) standard interconnects simple, low power and low processing capability wireless devices. The Zigbee devices facilitate numerous applications such as pervasive computing, national security, monitoring and control etc. An effective positioning of nodes in a ZigBee network is particularly important in improving the performance (e.g., throughput) of ZigBee networks. In the wireless sensor network (WSN) literature, the use of a mobile sink is often recommended as an effective defense against the so-called hot-spot phenomenon. But the effects of mobile coordinator on the performance of the network are not given due consideration. In this paper, we perform extensive evaluation, using OPNET Modeler, to study the impact of coordinator mobility on ZigBee mesh network. The results show that the ZigBee mesh routing algorithm exhibits significant performance difference when the router are placed at different locations and the trajectories of coordinator are varied. We also show that the status of ACK in the packet also plays a critical role in deciding network performances.