In this paper. we propose a method of confidence measure fusion under Bayesian framework for speech recognition. Centralized and distributed schemes are considered for confidence measure fusion. Centralized fusion is feature level fusion which combines the values of individual confidence scores and makes a final decision. In contrast. distributed fusion is decision level fusion which combines the individual decision makings made by each individual confidence measuring method. Optimal Bayesian fusion rules for centralized and distributed cases are presented. In isolated word Out-of-Vocabulary (OOV) rejection experiments. centralized Bayesian fusion shows over 13% relative equal error rate (EER) reduction compared with the individual confidence measure methods. In contrast. the distributed Bayesian fusion shows no significant performance increase.