The AlCrMoNbZr high entropy alloy (HEA) has potential applications as a high-performance cladding coating material. Here, we report the results about the vacancy defects in AlCrMoNbZr HEA using first-principle calculations. We have explored the variations in bulk and vacancy defect properties due to different local chemical environments in AlCrMoNbZr HEA with and without B/Hf doping, using both supercell and special quasi-random structures (SQS) techniques. Vacancy formation energy (VFE) is analyzed in accordance with the statistical distribution across three systems. The VFE exhibits a broad range of values and is characterized by a normal distribution. It is also significantly influenced by the type of doping atoms and the type of vacancy. Specifically, B doping substantially reduces the vacancy formation energy, thereby facilitating the formation of vacancies. Furthermore, the doping of B and Hf exerts a considerable impact on the formation of Zr vacancies (Zr_Vac) and Mo vacancies (Mo_Vac). In addition, Al vacancies (Al_Vac) are most readily formed in the AlCrMoNbZr HEA, while Mo vacancies (Mo_Vac) are most easily formed following the introduction of B and Hf dopants. The VFE in AlCrMoNbZr HEA with and without Hf dopant increases with the increase of the number of Cr and Mo atoms in the local chemical environment, and decreases with the increase of the number of Zr atoms. In conclusion, B doping promotes the formation of vacancy, which is not conducive to the improvement of initial irradiation resistance performance. Fortunately, one can infer from the results of the effect of local chemical environment on VFE that it is rewarding in improving the initial irradiation resistance by increasing the occurrence of Mo-Mo and Zr-Zr arrangement in AlCrMoNbZr HEA.