The analysis of structural change in the time series data which has the long-memory property is important because the long-memory property may possibly be caused by structural change. We develop a new Bayesian method for the estimation of the autoregressive fractionally integrated moving average (ARFIMA) model with multiple structural changes. The most widely used for the Bayesian analysis of structural change is the irreversible Markov switching model but it requires us to use the Hamilton filter, which is not applicable to the ARFIMA model because of the path dependence problem. Instead of using this model, we treat change points as parameters and sample them as well as the parameters in the ARFIMA model from the joint posterior distribution using a Markov chain Monte Carlo (MCMC) technique. Specifically, we use the differential evolution adaptive Metropolis (DREAM) algorithm and its discrete version (D-DREAM). We illustrate our method by applying it to the realized volatility of the Nikkei 225.