Existing research in transport protocols for wireless ad-hoc networks has focused on reliable end-to-end packet delivery under uncertain channel conditions, route failures due to node mobility and link congestion. In a cognitive radio (CR) environment, there are several key challenges that must be addressed apart from the above concerns. The intermittent spectrum sensing undertaken by the CR users, the activity of the licensed users of the spectrum, large-scale bandwidth variation based on spectrum availability, and the channel switching process need to be considered in the transport protocol design. In this paper, a window-based transport protocol for CR ad-hoc networks, TP-CRAHN, is proposed that distinguishes each of these events by a combination of explicit feedback from the intermediate nodes and the destination. This is achieved by adapting the classical TCP rate control algorithm running at the source to closely interact with the physical layer channel information, the link layer functions of spectrum sensing and buffer management, and a predictive mobility framework that is developed at the network layer. To the best of our knowledge, this is the first work on the transport layer to specifically address the concerns of the CR ad-hoc networks and our approach is thoroughly validated by simulation experiments.