This paper investigates distributed medium access control (MAC) to achieve rate guarantee in pulse-based time-hopping ultra-wideband (UWB) wireless networks, where the inherent spread spectrum supports simultaneous transmissions. In specific, we propose a transmission frame structure for the distributed MAC tailoring to the UWB characteristics, and develop a novel control message exchange procedure. Furthermore, we propose an effective distributed resource allocation algorithm to achieve high efficiency. The proposed distributed MAC can solve the near-sender-blocking problem and alleviate the negative effect of long acquisition time in UWB transmissions. Extensive simulations demonstrate the superior performance of the distributed MAC.