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In this letter, we propose a Student's t-hidden Markov model with truncated stick-breaking priors (TSB-SHMM). In the TSB-SHMM, the priors for elements in the initial state vector and the state transition matrix are constructed by stick-breaking procedure with a truncation level, and the observation emission distributions are the Student's t-mixtures. Then we derive an inference algorithm for estimating the parameters of the proposed TSB-SHMM. Experimental results on the synthetic data and text-dependent speaker identification illustrate that the TSB-SHMM can automatically determine the number of states and are robust to untypical observed data.