We report on an apodization scheme for terahertz fiber Bragg gratings. The grating consists of only 90 ablated notches on two opposite sides of a subwavelength polymer fiber. The grating strength can be effectively tuned by controlling the longitudinal shift between the two-sided notches, and apodization can be achieved by applying an envelope profile. Side lobe suppression of 14 dB was experimentally observed when compared with an unapodized grating.