The magnetic relaxation phenomenon is a crucial subject for the engineering applications of bulk hightemperature superconductors (HTS) in which the trapped field or levitation force behaves with a time-dependent decay due to the intrinsic flux creep inside the HTS materials. To fully exploit the high trapped field of bulk HTS, we have experimentally investigated the trapped flux relaxation properties, especially at different magnetization levels. With different excitation fields, the dependence between trapped field and relaxation rate was analyzed and compared in both field-cooling magnetization (FCM) and zero-fieldcooling magnetization (ZFCM) conditions. In parallel, the relaxation rates for different trapped flux can be measured all at once during a single magnetization process. The relaxation rate is closely correlated to the trapped field and useful to reflect the effect of the following remagnetization processes. To suppress the relaxation, we further checked possible methods from the three aspects of material improvement, working temperature and flux annealing effect.