In this paper, a novel hierarchical beamtracking approach, which is suitable for terahertz (THz) wireless systems, is presented. The main idea is to employ a prediction based algorithm with a multi-resolution codebook, in order to decrease the required overhead of tracking and increase its robustness. The efficiency of the algorithm is evaluated in terms of the average number of pilots and mean square error (MSE) and is compared with the corresponding performance of the fast channel tracking (FCT) algorithm. Our results highlight the superiority of the proposed approach in comparison with FCT, in terms of tracking efficiency with low overhead.