In this paper, we introduce a fast approach for Bayesian detection of change points in long-memory processes. Since a heavy computation is needed to evaluate the likelihood function of long-memory processes, a method for simplifying the computational process is required to efficiently implement a Bayesian inference. Instead of estimating the parameter, we consider selecting a element from the set of possible parameters obtained by categorizing the parameter space. This approach simplifies the detection algorithm and reduces the computational time to detect change points. Since the parameter space is (0, 0.5), there is no big difference between the result of parameter estimation and selection under a proper fractionation of the parameter space. The analysis of Nile river data showed the validation of the proposed method.