In polar materials, the transition of electrons in momentum space will change the spontaneous polarization. When excited by femtosecond pulse laser, the transient modulation of the electric polarization will radiate electromagnetic wave at terahertz frequency. In a magnetic ordered system, the coherent excited spin wave radiates electromagnetic waves of the same frequency in the process of precession and relaxation. The investigation of the terahertz emission spectra of these materials not only helps us to understand the ferroelectric and magnetic ordered dynamic processes of materials, but also provides a reference for searching for new terahertz sources. We study the terahertz emission spectrum of the polar antiferromagnet Fe ₂Mo ₃O ₈. Under the pumping of 800 nm laser, electrons in the material are excited across the band gap leading the electric polarization to be ultra-fast modulated. The broadband terahertz excitation spectrum from 0.1 to 3.5 THz is observed, and the direction of the terahertz electric field is along the inherent electric polarization direction of the material. After entering into the magnetic order state, two new single-frequency terahertz oscillations are observed, located at 1.25 THz and 2.7 THz respectively, which correspond to the excitation of the two antiferromagnetic spin waves of Fe ₂Mo ₃O ₈.