HMM (Hidden Markov Model) is widely used in pattern recognition areas such as speech and speaker recognition, handwritten recognition, gesture recognition, and so on. In this paper, we present a reliability-weighted HMM (RW-HMM) approach considering inexact observations. We introduce a weighting factor - confidence measures of observations - in HMM target function and drive a training algorithm based on the traditional EM (Expectation Maximization) algorithm for optimizing a modified HMM target function. To verify the usefulness of our proposed method, we performed SI (speaker identification) experiments using ETRI speaker recognition database. With the proposed RW-HMM, the experimental results show that the performance of SI is highly enhanced particularly in noisy environments. Finally, RW-HMM could be applied in any applications with well-defined reliability.