Resistance random access memory (RRAM) based on resistive switching in metal oxides has attracted considerable attention as a promising candidate for next-generation nonvolatile memory due to its high operating speed, superior scalability, and low power consumption. However, some operating parameters of RRAM cannot meet the practical requirement, which impedes its commercialization. A lot of experimental results show that doping is an effective method of improving the performance of RRAM, while the study on the physical mechanism of doping is rare. It is generally believed that the formation and rupture of conducting filaments, caused by the migration of oxygen vacancies under electric field play a major role in resistive switching of metal oxide materials. In this work, the first principle calculation based on density functional theory is performed to study the effects of transition metal element X (X=Mn, Fe, Co, and Ni) doping on the migration barriers and formation energy of oxygen vacancy in ZnO. The calculation results show that the migration barriers of both the monovalent and divalent oxygen vacancy are reduced significantly by Ni doping. This result indicates that the movement of oxygen vacancies in Ni doped ZnO is easier than in undoped ZnO RRAM device, thus Ni doping is beneficial to the formation and rupture of oxygen vacancy conducting filaments. Furthermore, the calculation results show that the formation energy of the oxygen vacancy in ZnO system can be reduced by X doping, especially by Ni doping. The formation energy of the oxygen vacancy decreases from 0.854 for undoped ZnO to 0.307 eV for Ni doped ZnO. Based on the above calculated results, Ni doped and undoped ZnO RRAM device are prepared by using pulsed laser deposition method under an oxygen pressure of 2 Pa. The Ni doped ZnO RRAM device shows the optimized forming process, low operating voltage (0.24 V and 0.34 V for Set and Reset voltage), and long retention time (>104 s). Set and Reset voltage in Ni doped ZnO device decrease by 80% and 38% respectively compared with those in undoped ZnO device. It is known that the density of oxygen vacancies in the device is dependent on the oxygen pressure during preparation. The Ni doped ZnO RRAM device under a higher oxygen pressure (5 Pa) is also prepared. The Ni doped ZnO RRAM device prepared under 5 Pa oxygen pressure shows a little higher Set and Reset voltage than the device prepared under 2 Pa oxygen pressure, while the operating voltages are still lower than those of undoped ZnO RRAM. Thus, the doping effect in the ZnO system is affected by the density of oxygen vacancies in the device. Our work provides a guidance for optimizing the performance of the metal oxide based RRAM device through element doping.