Global time synchronization is an important function that enables all devices in a network to have a unified time. In traditional wireless ad hoc networks, since the spectrum is always available, the global time synchronization process usually can be performed without any interruption. However, in cognitive radio (CR) ad hoc networks, the global time synchronization process among secondary users may fail due to the dynamic spectrum availability. Therefore, the network performance will be significantly affected if time synchronization fails. In this paper, the unique challenges in global time synchronization in CR ad hoc networks are addressed. A novel distributed global time synchronization protocol is proposed considering the unique features of CR ad hoc networks such as the traffic and the topology of primary users (PUs). An optimal root node (i.e., the node which provides the reference time) selection scheme and an optimal time synchronization period are designed. Moreover, under the proposed optimal root node and the optimal time synchronization period, the synchronization delay and the impact of PUs on the global time synchronization performance are reduced dramatically. To the best of our knowledge, this is the first paper that investigates the global time synchronization issue in CR ad hoc networks that considers the unique features of CR ad hoc networks.