The programming speed of charge trapping memories (CTM) with different defects were studied based on the first principle and VASP package. The defects include threefold oxygen vacancy (VO3), fourfold oxygen vacancy (VO4), hafnium vacancy (VHf), and interstitial oxygen (IO). Trapping energy, energy band offset, and the trapping density were calculated and compared. Results show that VO3, VO4 only trap holes, VHf only trap electrons, and IO trap electrons and holes; the most important is the trapping energy which is greater in VHf. It is the best for trapping charges; because the charge tunneling into trapping layer is easy in VHf. It can also reduce the tunneling time. Finally, the trapping densities were compared with each other: VHf's trapping density is greater than other defects, i.e. charges can be trapped easier than by other defects. All of these show that VHf is the best one for reducing programming time. This paper will provide a theoretical guidance for increasing the programming speed ofCTM.