This article presents a robust variational Bayesian (VB) algorithm for identifying piecewise autoregressive exogenous (PWARX) systems with time-varying time-delays. To alleviate the adverse effects caused by outliers, the probability distribution of noise is taken to follow a t -distribution. Meanwhile, a solution strategy for more accurately classifying undecidable data points is proposed, and the hyperplanes used to split data are determined by a support vector machine (SVM). In addition, maximum-likelihood estimation (MLE) is adopted to re-estimate the unknown parameters through the classification results. The time-delay is regarded as a hidden variable and identified through the VB algorithm. The effectiveness of the proposed algorithm is illustrated by two simulation examples.