The dielectric properties of single-crystal MgO were studied by terahertz time-domain spectroscopy in the frequency range extending from 0.5 to 9.5 THz. The refractive index, power absorption, and the complex dielectric function were extracted from experimental data. At low terahertz frequencies band (<2 THz), the absorption coefficient was extremely low and increased with increasing frequency. Meanwhile the corresponding refractive index had low dispersion, increasing from 3.12 to 3.15. Two prominent resonances were observed at 3.16 THz and 8.11 THz and were well-described by a multiple-oscillator model through theoretical fitting. The interaction of incident photons and the transverse optical (TO) phonons in the crystal were studied and it gives good evidence to further applications in developing broadband terahertz components and terahertz spectroscopy.