Item response theory (IRT) is a modern test theory that has been used in various aspects of educational and psychological measurement. The fully Bayesian approach shows promise for estimating IRT models. Given that it is computationally expensive, the procedure is limited in practical applications. It is hence important to seek ways to reduce the execution time. A suitable solution is the use of high performance computing. This study focuses on the fully Bayesian algorithm for a conventional IRT model so that it can be implemented on a high performance parallel machine. Empirical results suggest that this parallel version of the algorithm achieves a considerable speedup and thus reduces the execution time considerably.