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. This article develops a method for the analysis of multiple structural changes in such data. The irreversible Markov switching model proposed by Chib (1998) is incorporated in the autoregressive fractionally integrated moving average (ARFIMA) model. The Hamilton filter is no longer applicable to the resulting model because the ARFIMA model is an AR model with infinite lag-length. A Bayesian method is developed where the parameters and the state variable representing the number of structural changes up to each period are sampled from their posterior distribution using the particle Markov chain Monte Carlo method proposed by Andrieu et al. (2010). The marginal likelihood is used for selecting the number of change-points and analyzing whether the long-memory property is spuriously caused by structural change or not. Several researchers have documented that the realized volatility (RV) defined as the sum of squared intraday returns has the long memory property. The proposed method is illustrated by applying to the RVs of several financial returns.