Thread migration is ubiquitous in multi-core architectures. When a thread migrates to an idle core, the branch information of the branch predictor on the idle core is absent, which will lead to the branch predictor works with comparatively low prediction accuracy until the warm-up finish. During the warm-up period, the branch predictor spends quite a lot of time on recording branch information and often makes mispredictions. These are the main performance impact of thread migration. In this paper, we point out that, when a thread migrates to an idle core, the prediction accuracy can be improved by migrating branch history information from the source core to the target. Moreover, several migration strategies are introduced to fully exploit the performance of branch prediction migration. Experiment results show that, compared to the experiment baseline which doesn’t migrate any branch history information, branch prediction migration reduces MPKI of the branch predictor on new core by 43.46% on average.