With its capability of supporting high data rate services in a short range, the Ultra-Wide Band (UWB) technology is appealing for future wireless personal area networks (WPANs). However, the WPAN Medium Access Control (MAC) protocol in IEEE 802.15.3 standard was originally designed for narrow band communication networks, and it is inherently in-efficient for UWB networks. In this paper, we explore the unique characteristics of UWB communications and propose how to schedule concurrent transmissions in UWB networks, which can significantly improve efficiency and network capacity. Since the optimal scheduling problem for peer-to-peer concurrent transmissions is NP-hard, the induced computation load for solving the problem is not affordable to the network coordinator, commonly a normal UWB device with limited computation power and energy. We propose two simple heuristic scheduling algorithms with polynomial time complexity. Extensive simulations with random network topology demonstrate that, by allowing concurrent transmissions appropriately, the proposed scheduling algorithms can significantly increase the network throughput.