Hidden Markov model (HMM) adaptation is currently of interest, to overcome the degradation effect of speaker and/or channel mismatches in practical speech recognition systems. The Bayesian framework provides a theoretically optimal formulation for combining adaptation data and prior knowledge, but it suffers from the drawback of being incapable of adapting parameters of the models that have no observations in the adaptation speech. In this article we present a new predictive (in the sense of influencing unobserved distribution parameters) adaptation algorithm for the mean vectors of an HMM. We also point out some theoretical relationships between the proposed method and other techniques used in the context of predictive model adaptation. The efficacy of the proposed approach is demonstrated in speaker adaptation experiments for both an isolated word task, and TIMIT phonetic recognition.