Dielectric spectral technique is the technique to analyze microstructural changes by means of macroscopic dielectric parameters. Compared with microwave ones, terahertz dielectric spectra contain rich fingerprint information and can reflect multiple motion modes within materials. In this paper, the dielectric spectra in the terahertz spectral band of natural rubber after thermal aging are investigated and the corresponding changes in the molecular structures are further analyzed. The research results show that both the real and imaginary parts of terahertz dielectric constants of samples possess definite change laws, which is corresponding to the microstructural changes during aging of materials. In addition, the acquired terahertz dielectric spectral data is fitted to obtain the corresponding dielectric constant at zero frequency, dielectric constant at optical frequency and dielectric strength. From the standpoint of overall structures of molecules, the relationship of the polar structures and intermolecular network structures during aging with the decomposition and crosslink of molecule chains is analyzed. The research conclusion indicates that terahertz dielectric spectra have potential application value in non-destructive detection of aging materials.