This paper develops a variational Bayesian approach for identifying ARX models with missing observations and varying time-delays. The outputs of the ARX models are subject to both slow sampling rates and communication delays. The unknown missing observations which are used in the variational Bayesian approach can be estimated by a modified Kalman filter, and based on the estimated missing observations and available data, the unknown parameters and the varying time-delays can be estimated by using the variational Bayesian approach. The simulation results demonstrate that the variational Bayesian method is effective. (C) 2018 Elsevier Ltd. All rights reserved.