It is particularly attractive for High Temperature Superconductors (HTS), such as the melt-processed YBCO single-grain bulks, to trap strong magnetic fields at cryogenic temperatures. With the flux density orders of magnitude much greater than the rare earth magnets, the YBCO bulks can be formed as small and as compact as them. As a result, YBCO bulks are used as magnets in magnetic bearings, MRI scanners and motors, etc. The trapped field by the YBCO magnet is decided by the magnetization, which normally includes three different ways. However, the traditional ways to magnetize the YBCO will always need the applied field to be as high as the expected field on the superconductor or much higher than it. In this paper, we will describe a technique which facilitates the creation of the high magnetic field and utilize a normal permanent magnet in stead. By using this rare earth permanent magnet which is not as strong, this technique involves the superconducting flux pump concept, which means that a much larger field being trapped by the superconductor bulk is caused by a small field repeatedly applied to it. To achieve such pumping effect, an intermedia material is necessary and in the related experiments, Gadolinium is used as such an important thermally actuated material. Traveling magnetic field through it will magnetize the YBCO in such a way that the flux density will be accumulated step by step on the surface on the bulk.