In this article, an approach for identification of an errors-in-variable system whose output is contaminated by heteroscedastic noise is developed. A Markov chain is applied to depict the correlation of the switching of heteroscedastic noise model. The estimation of model parameters adopts a variational Bayesian algorithm. The advantage of the Bayesian approach is the full probability description of the estimates while the classical expectation-maximization algorithm only provides point estimation. A simulated numerical example and an experimental study on a polyester fiber process are provided to demonstrate the effectiveness of the proposed method. Three performance indexes, normalized mean-absolute error, mean-relative error and root-mean-squared error, are used to evaluate the performance of the proposed algorithm. Meanwhile, Monte Carlo cross validations are performed to demonstrate the effectiveness and superiority of the proposed algorithm.