Materials exhibiting a drastic change in electrical resistivity depending on magnetic-field direction is of great interest and is rarely seen in real systems. We report the huge anisotropic magnetoresistance ratio exceeding 7500 at low-magnetic field of 0.4 T at 2 K in the layered magnetic semiconductor ${\mathrm{CeTe}}_{1.83}{\mathrm{Sb}}_{0.17}$ with extremely low carrier density in charge-density-wave state. We found that the electrical resistivity is governed only by the out-of-plane component of magnetization and steeply decreases nearly four orders of magnitude in the magnetic field along the $c$ axis. In contrast, it is quite insensitive to the in-plane component of magnetization and huge anisotropy is preserved even in a much higher magnetic field.