In this paper, we study a class of robust automatic speech recognition problem in which mismatches between training and testing conditions exist but an accurate knowledge of the mismatch mechanism is unknown. The only available information is the test data along with a set of pretrained speech models and the decision parameters. We try to compensate for the abovementioned mismatches by jointly adopting a dynamic system design strategy called on-line Bayesian adaptation to incrementally improve the estimation of the model parameters used in the recognizer, and a robust decision strategy called Bayesian predictive classification to average over the remaining uncertainty in model parameters. We report on a series of experimental results to show the viability and effectiveness of the proposed method.