Polymer materials such as rubber and plastics are prone to aging induced degradation, especially thermo-oxidative aging. In this paper, terahertz time-domain spectroscopy was employed to investigate the aging process of styrene butadiene rubber by spectrally following the evolution of its dielectric permittivity in the terahertz frequency region during prolonged high-temperature, accelerated, continuous thermo-oxidative aging. The real and imaginary parts of the dielectric constant in the 0.1-0.8THz frequency band were obtained and analyzed, and shown to be consistent with present theoretical understanding. The study revealed a close relationship between the evolution of the rubber's dielectric permittivity and the material's physical response to the terahertz electromagnetic radiation during thermo-oxidative aging, manifesting a strong correlation between quantitative changes of the dielectric permittivity and the degree of aging, which can be understood qualitatively in terms of dynamical structural changes at the molecular level.