The effect of local chemical environment (i.e., type and content of atom neighboring to defects) on the point defect properties has been thoroughly investigated in bcc AlNbTiZr refractory high-entropy alloys (HEAs). It has been shown that the randomness of local chemical environments in AlNbTiZr HEAs leads to a wide distribution of vacancy and interstitial formation energy rather than to definitive values. One interesting aside here is that the number of Al and Nb atoms locating at the first-nearest neighbor (1nn) of vacancy drives the evolution of vacancy formation energy (VFE) in AlNbTiZr system, as vacancies preferred Al-rich and Nb-poor environments. What another worth noticing is that the most stable interstitial defects are in the form of dumbbells. What's more, the Al-Al dumbbell is the easiest interstitial defect while the Zr-Zr dumbbell is the least according to the lowest formation energy and electronic characteristics. Along with the results of vacancies preferred Al-rich environments, Al in AlNbTiZr can stabilize the single vacancy and inhibit its migration and diffusion to form large-size vacancy clusters. Therefore, the initial irradiation resistance can be improved by adjusting the concentration and distribution of Al in AlNbTiZr. One can infer from the results obtained present that it is beneficial in improving the irradiation resistance by controlling different processing experimentally methods to increase the occurrence of Al-Al arrangement in AlNbTiZr high-entropy alloys.