In this paper, the sieve bootstrap test for multiple change points in the mean of long memory sequence is studied. Firstly, the ANOVA test statistics for change points detection is obtained. Secondly, sieve bootstrap statistics is constructed and the consistency under the Mallows measure is proved. Finally, the effectiveness of the method was illustrated by simulation and example analysis. Simulation results show that our method can not only control the empirical size well but also have reasonable good power.