This paper presents a method to track multiple moving humans using Ultra-Wideband (UWB) radar. UWB radar can complement other human tracking technologies, as it works well in poor visibility conditions. Our tracking approach is based on a point process interpretation of the multi-path UWB radar scattering model for moving humans. Based on this model, we present a multiple hypothesis tracking (MHT) framework for tracking the ranges and velocities of a variable number of moving human targets. The multi-target tracking (MTT) problem for UWB radar differs from traditional applications because of the complex multipath scattering observations per target. We develop an MHT framework for UWB radar-based multiple human target tracking, which can simultaneously solve the complex observation clustering and data association problems using Bayesian inference. We present experimental results in which a monostatic UWB radar tracks both individual and multiple human targets to estimate target ranges and velocities, even with changing numbers of targets across radar scans.