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The Cox-Ingersoll-Ross (CIR, 1985) model is one of the most widely used for modeling the term structure of interest rates. Since it is a non-linear and non-Gaussian state space model, it is difficult to estimate the parameters using the maximum likelihood method. This paper presents an efficient Bayesian method for the estimation of the CIR model using Markov-chain Mote Carlo (MCMC) techniques. Following Sanford and Martin (2003), we approximate the continuous-time square root process for the short rate by a discrete-time model using the Euler discretization. They use a single-move sampler to sample the state variables and a random-walk Metropolis-Hastings algorithm to sample the parameters, both of which are inefficient in the sense that they would produce a highly correlated sample sequence, making the speed of convergence slow and the standard errors of estimates large. To reduce this inefficiency, we use the block sampler proposed by Omori and Watanabe (2003) and an independence Acceptance-Rejection Metropolis-Hastings algorithm. Using the simulated data, we show that our method performs well. We also apply our method to the U.S. term structure data.