Abstract: In this paper, the eigen equation is utilized to study the high-order mode coaxial resonant cavity operating in the terahertz (THz) band, the cavity's resonant frequencies of TM_{m, 1, 0} mode, TM_{m, 2, 0} mode and TM_{m, 1, 1} mode associating with the geometric parameters are discussed, and the evidence for selecting the operating mode is presented. On this foundation, a new type of 0.3 THz TM_{10, 1, 0} mode coaxial coupled cavity chain is proposed, analyzed by equivalent circuit and simulated by CST-MWS simulation software. Its properties of cold cavity such as dispersion characteristic, characteristic impedance and electric field pattern are presented. In addition, the effect of the geometric parameters on the dispersion characteristic and the characteristic impedance is analyzed and summarized emphatically. The results of the study indicate that, TM_{10, 1, 0} mode is a reasonable operating mode for the THz high-order mode coaxial coupled cavity chain. The 0.3 THz TM_{10, 1, 0} mode coaxial coupled cavity chain operating in the 2π cavity mode has a large characteristic impedance, but the frequency spacing between the modes is small, so it can be applied to a narrow-band terahertz extended interaction device. Increasing the angle of the coupling slot is the best way to increase the mode spacing.