Practical impulse radio ultra-wideband (IR-UWB) ranging systems always have to work in multi-user and weak non-line-of-sight (NLOS) environments. In this paper, we derive a novel IR-UWB ranging estimator under multi-user and weak NLOS environments. We model MUI with complex Gaussian mixture model (CGMM) in the frequency domain. We propose a novel estimator for the UWB time of arrival (ToA) parameters based on the expectation maximization (EM) algorithm, the pseudo quadratic maximum likelihood (PQML) algorithm and CGMM. The estimator reduce the MUI in the frequency domain so that the cost function becomes asymptotically noiseless. Ranging is obtained by translating the obtained delay estimates into an estimate of the distance. And numerical evaluations under IEEE 802.15.3a channel model are presented to demonstrate the good performance of the proposed estimator.