Gibbs sampler, a typical Markov chain Monte Carlo (MCMC) method that approximately solves the Bayesian problem by simple numerical computation in a completely different paradigm was previously employed for the Bayesian detection in synchronous CDMA system. To perform the Bayesian detection for the asynchronous uplink CDMA system with unknown multiuser interference and multipath fading, the Gibbs sampler combined with the linear group-blind decorrelator is proposed as a novel Bayesian multiuser detection technique in this paper. Furthermore, in the study of the effect of channel estimation error on the performance of the proposed detector, we also present an iterative Bayesian multiuser detector where more accurate parameter estimation is achieved to improve the detection performance. Simulation results verify the effectiveness of the proposed detectors. The proposed detection techniques have the advantages of low complexity, high performance and wide applications.