In the past decade, Gaussian mixture regression (GMR) has become one of the most successful methods used for the monitoring of multivariate systems. One of the major limitations in GMR is its lack of robustness to outliers, since the estimates of the means and the precisions can be severely affected by atypical observations. Another issue is the infinite trouble, which is using maximum likelihood to fit a Gaussian mixture model (GMM). To resolve these issues of GMR-based methods, a novel Bayesian robust regression (BRR) is proposed for the automatic supervision of a nonlinear process. Specifically, a prior is placed on the mixture component in order to identify outliers in the process. Moreover, a separate precision weight is used for the inverse covariance matrix to address the infinite trouble. The predictive distribution obtained by the variational Bayesian inference is a Students t distribution, which makes the model more robust. The theoretical findings are fully supported by an empirical study performed on an artificial data set. Moreover, the comparisons of monitoring results on a simple nonlinear system and the benchmark Tennessee Eastman process demonstrate that the BRR-based process monitoring method is superior to the classical methods, such as principal component analysis (PCA) and kernel principal component analysis (KPCA).