Terahertz radiation as an upcoming carrier frequency for next-generation wireless communication systems has great potential to enable ultra-high-capacity transmissions with several tens of gigahertz bandwidths. Nevertheless, dispersion is one of the main impairments in achieving a higher bit rate. Here, we experimentally demonstrate a compact terahertz dispersion compensator based on subwavelength gratings. The gratings are fabricated from the low-loss cyclic olefin copolymer exploiting micro-machining fabrication techniques. With the strong index modulation introduced in the subwavelength grating, the high negative group velocity dispersion of -188 (-88) ps/mm/THz is achieved at 0.15 THz for x-polarization (y-polarization), i.e., 7.5 times increase compared to the state-of-the-art reported to date for terahertz. Such high negative dispersion is realized in a grating of 43 mm length. The asymmetric cross-section and periodic-structural modulation along propagation direction lead to considerable birefringence that maintains and filters two orthogonal polarization states, respectively. These polymer-based birefringent gratings can be integrated into terahertz communication systems for dispersion compensation of both long-haul wireless links and waveguide-based interconnect links.