Detailed measurements of the Hall effect in the paramagnetic phase of Ho 0.8 Lu 0.2 B 12 antiferromagnet at the magnetic field up to 80 kOe in the temperature range of 1.9–300 K have been performed. It has been found that the transition to the cage glass phase ( T < T  * ~ 60 K) is accompanied by the appearance of a positive Hall resistance component in addition to that corresponding to the negative Hall effect. The amplitude and angular dependence of the former depend on the magnitude and direction of the applied magnetic field with respect to the crystallographic axes. The revealed anisotropy of the Hall effect in Ho 0.8 Lu 0.2 B 12 is attributed to the interaction of charge carriers with dynamic charge stripes.