We propose a robust iterative multiuser receiver for decoding convolutional coded code-division multiple access (CDMA) signals in both Gaussian and non-Gaussian channel noise. The receiver is derived from a modified maximum a-posteriori (MAP) algorithm called the max-log-MAP algorithm for robustness against erroneous channel variance estimation. Furthermore, the effect of destructive outliers arising from impulsive noise is mitigated in the proposed receiver by incorporating the robust Huber penalty function into the multiuser detector. The proposed receiver is shown to perform satisfactorily over Gaussian and non-Gaussian impulsive channels. In every iteration, cumulative improvement in the quality of the a-posteriori probabilities is also demonstrated.